The debt limit is suspended until March 15, 2017, at which time it will be both reset to include all debt issued while it was suspended, and frozen at that level until it is raised or re-suspended. The Treasury should have enough cash to operate until at least August.
Usually it just gets suspended again without much of a fight. This time, however, the Republicans, being in the majority, could get tough, and the Democrats would love to trip Trump up.
The main question I have is will it reach $20 trillion before March 15?
See also: http://www.marketwatch.com/story/raising-the-debt-ceiling-is-now-trumps-problem-2017-02-01