Hey MerlotMonday,
Sorry to disagree with just about all of the above posts, but you actually DO have some power in this situation. Simply put, it is entirely reasonable for you to ask School A to commit to giving you funding by April 15. I suggest you inform School A of the following:
You have been offered a generous financial package elsewhere and need to either accept or deny their offer by April 15 at the absolute latest. Since school A is your top choice, if school A will match the funding offered you by school B, you will definitely attend school A. However, if school A is not able to make a funding offer comparable to that made by school B by April 15, you will regretfully have to attend School B.
Here's what will happen--either school A will come through in time and you will attend school A with full funding or school A will not come through and you will attend school B with full funding. If you want to go to school A with no funding or partial funding, well...that's up to you. If you have some secret reserves of cash somewhere or don't mind taking out loans, then that's your decision to make.
Under NO circumstance should you inform School B that they are your second choice, nor should you ask them to wait around for you until May. That's stupid. There are plenty of people who would LOVE to go to school B. Don't jerk them around.
AND before you do anything else, find a faculty mentor at your current school--maybe someone who wrote a rec letter for you--and ask them to help you negotiate this. They've been through this process, they know more, and some of them even really like to do this negotiation kind of stuff.
Good luck, MerlotMonday.