Be aware that recruiters are working for your new employer. Not for you. I find 99% of them to be slimeballs. On the hierarchal chart of salespeople, they're a step below used car salespeople.
You do what's right for you and not for your recruiter. That's bull that he needs to know an answer by an exact hour. It's a pressure tactic he probably picked up when he sold used Pontiac Aztecs.