Certainly they have the power to do so, but a certain Obama veto trumps that power. Since the Senate as currently constituted would never repeal, it makes little sense for the House to move forward on its own and risk the loss of any seats in November. Choose a battle that can be won, and then use the win to secure victory.
That battle will be to elect Mitt Romney, even if he wasn't your first choice, to the Presidency, and any Republican who commits to REPEAL Obamacare, to the House and Senate.