Republicans are not going to succeed in repealing Obamacare without control of the Senate and Obama still there to veto any such repeal. As such, I don't think they should bother. While I belive Obamacare is an abomination in its present form it can and should be improved and there are ways of doing so that provide opportunities for bipartisan cooperation.
1. Funding: Both parties are giving lipservice to the deficit. However, Republicans have stated that they do not want to raise marginal rates. On its face this appears hypocritical but it needn't be. One way to raise a significant amount of revenue would be to cap the employer exemption on healthcare and align the cap with the cost of a High Deductible Health Plan (HDHP) plan. This would have a significant and immediate impact on cost control thus reducing spending in the out years while raising more than letting the only the upper tax bracket of the Bush Tax Cuts (as the White House has proposed) expire would. This would also accelerate the transition away from an employer provided system.
2. Minimum Benefits: The current health care bill's principal failure is that it defines the minimum benefit in at a very high level. As such, most routine predictable care is paid by an insurer. Adding a party to a transaction is inefficient but also promotes overconsumption as prices are not immediately evident to the consumer. By capping the employer exemption more people would opt for HDHPs where routine non-catastrophic care comes out of pocket but Obamacare has effectively outlawed such plans by defining a high minimum benefit level. Reducing the minimum benefit level to a naked HDHP will also make the individual mandate more effective as the penalty (while staying the same) would be more significant in relationship to the much lower premiums of HDHP plan. This would ameliorate the potential adverse selection spiral that Obamacare presently appears destined for.
3. Exchanges: Accelerate implementation of the exchanges, allow individuals to buy into them as opposed to employers. Let individuals buy across state lines tomorrow. These three steps together would get employers out of the health care game. If employers are no longer providing health care this should make employees at the bottom end of the wage scale significantly cheaper and help with the unemployment picture.
These three elements would preserve the basic architecture of Obamacare, maintain the coverage expansions all while reducing the present and future cost of implementation.