Here was my situation. I turned in my application late February, a little too close to the deadline too. In fact, one of my letters of rec didn't get in on time. My prof contacted someone about really wanting to turn a letter for me, and the person replied that if a researcher would like to consider me for a position, will ask for the letter. So we crossed our fingers...
Eight weeks passed without hearing anybody... until April 18 I got an email from a reasearcher studying malaria who could possibly offer me a position. April 20 we had a phone interview; he had a sense of urgency because of "NIH stimulus package guidelines." At the end of our conversation, he cautioned that he could not, at the time, guarantee me a position because he wasn't sure if would get the funds. But on the next day, funding was approved and I got the internship!! How fast was that!
So, yes, I believe funding may have been tight, but the govt stimulus have changed that for the better.
I think I was VERY lucky, mostly because I didn't contact any researchers; I really didn't have any hopes of getting an internship.