So the new fiscal cliff date is approximately March 1, though that's not a hard date for the debt ceiling. There's also the matter of having an operating budget for the federal government, even in the form of a continuing resolution. The current continuing resolution runs out on March 27.
The budgeting fight is not over by any means. There are a number of deadlines that will now come up hard against the government, allowing deficit hawks the opportunity to try to drive better bargains with President Obama and other Congressional Democrats. So while this deal isn't a huge victory for deficit hawks or tax reformers, they will live to fight another day - specifically, for the next two months.