<p>Internship hiring depends on industry… consulting and financial services companies recruit in the spring (consulting usually starts a couple weeks later than FS); a friend who is in the oil industry lined up his internships starting in October when we were in college, since that many companies in that industry has summer interns secured by Christmas. </p>
<p>However, the OP is talking about a federal government internship, and timing there depends on the agency (I don’t know anything about those kinds of jobs, so I won’t pretend to be able to give advice on it).</p>