Would it be rude to put my professor's name in for a reference when they haven't responded yet? I asked this professor for a recommendation letter last admissions season, and got a yes immediately and was very good about sending in letters.

This year it's much much harder to get a hold of them, and haven't responded to my recommendation letter email that I sent yesterday (I only sent it late this time because I figured they'd say yes) and my first deadlines are tomorrow. Would it be rude to just put the name in anyway, assuming they don't reply tomorrow? They've done it before so I figure it wouldn't be a bother for them to just re-send letters, but I'm worried it would be rude. But my future is at stake here.

Update: It ended up working out; thanks for your help.
You should absolutely NEVER list somebody as a recommendation without permission. Its asking for trouble.  Your deadline issue is YOUR issue, not your recommenders.  If time is critical, you should have mentioned that in your earlier email.  You should consider a followup email, letting him know that time is critical, or even stop by is office or call.