Short answer: Nope.
Long answer: It's complicated.
The proportion of the work copied can actually be the whole of the work (i.e. 100%), if the other parts of the fair use test provide a strong enough justification:
The extent of permissible copying
varies with the purpose and character of the use. Taking more of the copyrighted work
than is necessary to accomplish the fair user’s salutary purpose will weigh against fair
use. In some cases, the fact that the entire work — for example, an image — was needed to
accomplish the fair use purpose has led the court to hold that the third factor was neutral,
favoring neither the copyright holder nor the putative fair user.
Copyright and Fair Use: A Guide for the Harvard Community, Harvard University Office of the General Counsel, Last Updated
November 23, 2009
Unfortunately, the courts haven't consistently viewed educational use as 'fair use' per se:
On its face, the text of the statute seems to favor educational uses of works as fair uses. It first lists a variety of educational purposes such as criticism, comment, teaching, scholarship, and research as prototypical fair uses. It then identifies the use of content for “nonprofit educational purposes” as an explicit consideration in the first of the four enumerated factors for consideration in a fair use analysis.
In practice, however, courts have not consistently found that educational uses qualify as fair uses. Because the doctrine is applied on a case-by-case basis and resists reduction to a per-se rule, it provides limited assurance to scholars and teachers seeking bright-line guidance. ... even scholars well-read in precedent may be hard-pressed to find consistent analyses, across different federal courts, of educational copying and other scholarly uses.
Digital Learning Legal Background Paper:
Fair Use and Educational Uses of Content, Ashley Aull for the Berkman Center for Internet and Society at Harvard Law School
So you need to look at how the other three parts of the test pertain in the particular case at issue.
Unfortunately, in regard to the first factor:
In determining whether a use is “commercial,” courts generally find that the “distinction is not whether the sole motive of the use is monetary gain but whether the user stands to profit from exploitation of the copyrighted material without paying the customary price.” Thus, despite the fact the statutory text contrasts commercial with nonprofit educational purposes, courts may exclude schools and universities from the protection of the fair use doctrine if they “benefit” from such uses.
Harper & Row Publishers, Inc. v. Nation Enterprises, 471 U.S. 539 (1984) as cited in Aull
And in regard to the fourth factor:
the Court has held that “a challenge [of a use]…requires proof either that the particular use is harmful, or that if it should become widespread, it would adversely affect the potential market for the copyrighted work.”
Sony Corp. of America v. Universal City Studios Inc., 464 U.S. 417 (1984) as cited in Aull.
We should therefore take account of a couple of facts that pertain in our hypothetical situation:
the student benefits from their use of the material,
if all students were to copy the material without paying for it then the market for the material would be destroyed, which would hurt the incentive system for the production of new works,
and those facts seem to me to imply that copying (or downloading a copy of) an entire textbook, where the alternative is paying to purchase the textbook, would usually not be 'fair use' under US law.
But exceptions to this are possible. If the whole work was vital for scholarship but not commercially available then a pretty strong argument for 100% copying as fair use could be made. For the full picture read Aull.
Update in response to comments:
@einpoklum, thanks for your insightful comments. I thought they deserved proper discussion, so I'm answering them here, where I've got more space to address them.
It seems that the complicated situation is more in the case of educational institutions using full cpies.
You're correct that the case law (at least as far as I'm aware) that's specifically about textbooks concerns organisations (such as businesses and educational institutions) rather than individuals.
That's likely to be because it's not worth suing an individual for a very small loss. If the textbook only costs $20 - or even if it costs $100 - the publisher would lose money by suing the student, because the non-recoverable costs of the case (such as the time of the publisher's staff) would cost more than that. This is the reason why lawsuits in P2P filesharing cases tend to be filed against the uploader rather than the downloader.
But has there ever been a conviction, or a ruling in a civil suit, against a student who downloaded a copy of a textbook?
Not that I'm aware of. The very small amount of damages that could be recovered would mean that this would be a loss-making lawsuit even if it were won, although it might have a certain deterrent effect.
"Can I get away with doing this without being sued?" (to which the answer is almost certainly 'Yup') is of course a different question from "Is it legal?".
Also, any copier of any work stands to benefit from it somehow, otherwise they wouldn't make the copy; it seems you're interpreting that sentence too widely.
It certainly is a very wide interpretation! Unfortunately this is the interpretation which the US courts seem to give it.
Aull makes this point as well:
of course, one might strain to find a situation in which educators would use content without benefiting from it somehow.
Aull, footnote 10, page 5.
The Guidelines for Classroom Copying have received the most scholarly and judicial attention. While recognizing that some photocopying of copyrighted material for classroom distribution is fair use, the Guidelines require that such copying, in addition to having clear copyright notice on each copy, fall within three specifically described limits: “brevity,” “spontaneity,” and “cumulative effect.” The American Association of University Professors and Association of American Law Schools vigorously opposed these Guidelines, stressing that they “restrict the doctrine of fair use so substantially as to make it almost useless for classroom teaching purposes.” Meanwhile, in a series of strategic lawsuits filed soon after the passage of the 1976 Act, publishing interests succeeded in persuading some courts to view those Guidelines as an authoritative gauge of fair use.
Also, your claim about market destruction is simply invalid - just like with the music industry, people continue to buy music, concert tickets etc. despite having downloaded copies off of the Internet.
This is a view with which I have much sympathy. Unfortunately the same cannot be said for the US courts.
An example from the Napster case:
- Effect of Use on Market ...
 Addressing this factor, the district court concluded that Napster harms the market in “at least” two ways: it reduces audio CD sales among college students and it “raises barriers to plaintiffs’ entry into the market for the digital downloading of music.” Napster, 114 F. Supp. 2d at 913. The district court relied on evidence plaintiffs submitted to show that Napster use harms the market for their copyrighted musical compositions and sound recordings. In a separate memorandum and order regarding the parties’ objections to the expert reports, the district court examined each report, finding some more appropriate and probative than others. A&M Records, Inc. v. Napster, Inc., Nos. 99-5183 & 00-0074, 2000 WL 1170106 (N.D. Cal. August 10, 2000). Notably, plaintiffs’ expert, Dr. E. Deborah Jay, conducted a survey (the “Jay Report”) using a random sample of college and university students to track their reasons for using Napster and the impact Napster had on their music purchases. Id. at *2. The court recognized that the Jay Report focused on just one segment of the Napster user population and found “evidence of lost sales attributable to college use to be probative of irreparable harm for purposes of the preliminary injunction motion.” Id. at *3.
 Plaintiffs also offered a study conducted by Michael Fine, Chief Executive Officer of Soundscan, (the “Fine Report”) to determine the effect of online sharing of MP3 files in order to show irreparable harm. Fine found that online file sharing had resulted in a loss of “album” sales within college markets. After reviewing defendant’s objections to the Fine Report and expressing some concerns regarding the methodology and findings, the district court refused to exclude the Fine Report insofar as plaintiffs offered it to show irreparable harm. Id. at *6.
 Plaintiffs’ expert Dr. David J. Teece studied several issues (“Teece Report”), including whether plaintiffs had suffered or were likely to suffer harm in their existing and planned businesses due to Napster use. Id. Napster objected that the report had not undergone peer review. The district court noted that such reports generally are not subject to such scrutiny and overruled defendant’s objections. Id.
 We, therefore, conclude that the district court made sound findings related to Napster’s deleterious effect on the present and future digital download market. Moreover, lack of harm to an established market cannot deprive the copyright holder of the right to develop alternative markets for the works. See L.A. Times v. Free Republic, 54 U.S.P.Q.2d 1453, 1469-71 (C.D. Cal. 2000) (stating that online market for plaintiff newspapers’ articles was harmed because plaintiffs demonstrated that “[defendants] are attempting to exploit the market for viewing their articles online”); see also UMG Recordings, 92 F. Supp. 2d at 352 (“Any allegedly positive impact of defendant’s activities on plaintiffs’ prior market in no way frees defendant to usurp a further market that directly derives from reproduction of the plaintiffs’ copyrighted works.”). Here, similar to L.A. Times and UMG Recordings, the record supports the district court’s finding that the “record company plaintiffs have already expended considerable funds and effort to commence Internet sales and licensing for digital downloads.” 114 F. Supp. 2d at 915. Having digital downloads available for free on the Napster system necessarily harms the copyright holders’ attempts to charge for the same downloads.
 Judge Patel did not abuse her discretion in reaching the above fair use conclusions, nor were the findings of fact with respect to fair use considerations clearly erroneous.
A&M RECORDS, Inc. v. NAPSTER, INC., 239 F.3d 1004 (9th Cir. 2001)
I'm hearing speculative opinions on the prospective interpretation of the law.
Yes, that's entirely correct. In the absence of an existing case which exactly replicates the hypothetical situation you're proposing, that's all that anyone can give you. If you want a probably-more-accurate speculative opinion then consult a lawyer, but it'll still just be their opinion.
That doesn't mean, though, that the law doesn't apply until there's been a case which covers exactly these circumstances.
In the mean time, it seems perhaps nobody has even been sued or tried criminally for doing this, and it is a widespread practice. So...
So you'd probably not be sued. That's correct, but doesn't mean that the practise is necessarily legal.
A few notes:
- You should also be aware that many US universities have their own rules which are more restrictive than copyright law:
more than 80 percent of American universities now adhere to internal policies derived from the Classroom Guidelines that university lobbying groups has rejected. Some enforce even stricter guidelines, all but prohibiting reliance upon fair use. At least one commentator has predicted that, in this environment, “current trends…will eventually eliminate fair use for schools, colleges and universities.”