Here's hoping they do! I believe that the Republicans were voted in to control spending, repeal Obamacare, and extend tax cuts. Admittedly the Republicans acted like drunk sailors on shore leave the last time they were in charge; hopefully they have learned their lesson and will realize that Government spending is really taking money from hard working citizens and handing it out to others. Additionally, any Republican that slips into spendthrift ways will surely be attached by the Tea Party and targetted for ouster.
Well the Democrats were too busy to do required work like writing a budget. One of the first things they have to do is write a budget for next year. It will be be easy to defund it until the White House turnover.
Not without control of the Senate
As jwellsy said, just don't fund it! Granted Republicans only have "control" over the House but they do have a say in funding programs. Don't like something, don't provide funding for it.
Anything the House tries to undo will shot down by the senate or vetoed by the President.
Will they try? I think they'll try to repeal just parts of it, such as the mandate to own insurance.
Yes, that will break the system, and no, they won't care.
Will that succeed? They might be able to get it past the senate by convincing a few Democrats to go along with it- after all, several Democrats were reluctant to vote for it in the first place, and many of the remaining ones will be nervous about loosing their seat, and might go along with it in order to have a bargaining chip of sorts with the voters back home. (Being 'a Democrat who helped repeal the health care law' would cut much of the support out from under any competition.)
Standready has a good point though; the president has veto power, and I'm sure he'll veto anything that repeals his 'historic accomplishment'.
I doubt they'll be able to raise enough support in the senate to be able to override the veto.
The only realistic challenge to the health care law would be through the courts - a constitutional challenge might well manage to take out parts of the law, leaving congress to either change it or repeal it. - And the Republicans now have the numbers to block any revised version of it from passing.
I honestly hope they don't repeal it. I don't agree with everything in it, but a lot of it is good. I hope they amend it and make some changes but don't blindly repeal it, that won't help anyone, especially those that need it most!