In general, you are the lead author. If you are keen to progress a paper, then you need take the lead. This may mean that you wont get as much feedback from your co-authors as you might want. But this is generally better than delaying a publication for months and months. I also find there is a real cost in having to get back in the zone on a paper that I'm leading when it is put on hold because of such issues.
I would typically give co-authors a specific timeframe to make a contribution. For example, I might say that I am going to submit the paper in four weeks, and thus, any feedback they can provide in the next two weeks would be most welcome. I'd also try to get feedback from them about when they might have time to have a look at it, and I'd try to arrange my own schedule for working on the paper so that I'm able to send something through for when they might be free.
Of course, this is something to be negotiated. Sometimes, co-authors may want or expect to have greater involvement. Or you may think that their input is worth waiting for.
The case where a student is the lead author is also another variant. In that case, the supervisor would have more influence over timelines. In this case, the student may also be relying on the supervisor more to make sure that the manuscript is ready for submission.
What about co-author consent? Nate Eldredge raised the following issue in comments:
Don't you need the consent of all co-authors in order to submit a paper? So if they don't respond by your deadline, I don't see how you can ethically go ahead and submit anyway.
I agree that co-authors need to consent to having their name listed on a paper. That is very important. And you can imagine situations where consent would be an issue.
However, from my experience, in many situations the consent is implied. First, co-authors have usually already agreed to be involved in a publication at the start of the project. And in the above case, the co-authors have already submitted a paper and now they are revising it to submit it again. It's common for one author to take the lead on these kinds of revisions.
Then in the usual case, the lead author will send emails to co-authors outlining a publication plan with a timeline as well as follow-up emails as it gets closer to submission. The lead author would also send emails about when a submission occurs and when the status of the manuscript changes. At every stage, co-authors are free to negotiate the timeline, their input, and whether they wish to remain a co-author.
In most cases, co-authors respond to emails. Busy co-authors may not have time to actually make a contribution to the paper at that time, but any reasonable co-author will reply to emails in a reasonable time at least indicating their intentions about the paper (or they should have an auto-reply to say they are on leave). Furthermore, a submission is not the final word on authorship. For example, if a co-author didn't respond to emails for four weeks and then finds out their name was put on a submission that they did not approve of, there will still usually be plenty of time to withdraw their name, or make sufficient changes at the revisions stage.
So, I think if the lead author engages in reasonable correspondence about the publication plan and the submission process, then the issue can be navigated.