It definitely has. And by that, it has an impact even on academic life outside of the US. One of the most important data and literature resource in medical and life science is the US National Center for Biotechnology Information, running for example the literature database PubMed. Now it has a statement on its website saying
Due to the lapse in government funding, the information on this web site may not be up to date, transactions submitted via the web site may not be processed, and the agency may not be able to respond to inquiries until appropriations are enacted.
Concerning the National Institute of Health, the website http://www.usa.gov/shutdown.shtml states that
Research into life-threatening diseases and other areas will stop, and new patients won’t be accepted into clinical trials at the National Institutes of Health
I'm not sure how to interpret this, but it could mean that the research personnel is on unpaid leave.