sounds like your people may just walk you out that day, in which case there's a chance you'd get paid for the last two weeks anyway. If they want you to stay, they should be able to figure out a way of "client transitioning", which the clients may appreciate.
Finally, your new employer may wonder about circumstances if you just accepted the job and started the next day. If you can honestly say your old employer walked you out that day, you're better off. It may be a tight industry, especially if you're staying in the area.