The road to recovery for the Republican party begins with allowing a universal health care bill to pass. Ideally, they should aim for a working yet imperfect bill that passes with mild bipartisan support. This will allow Republicans to say that they supported the idea of health care while still allowing them to place the blame for any problems (and there are always problems in large scale reform) on the Democrats. The GOP needs health care reform to pass for three reasons: unions, small businesses, and votes.
The Republican Party does not like labor unions, and the feeling is mutual. Voters who have family members in a union are 8% more likely to vote for Democrats. Labor unions also raise millions of dollars for Democratic candidates. As a result, many in the GOP believe that labor unions are bad for business, corrupt, and antiquated. There is a reasonable argument to be made that most of the goals of the labor-movement have already been achieved. The five-day work week, worker's compensation, work place safety, the end of child labor, etc... have all been cemented into law. Health care remains almost the only justification for the maintaining or starting of labor unions. If every American were guaranteed access to affordable health care, labor unions will lose their main draw.
Small business owners tend to vote more heavily for Republicans. The message of lower taxes, self reliance, and less government interference has a strong appeal to this group of voters. The goal of the GOP should be to expand the number of small business owners as much as possible. The lack of affordable health care prevents thousands of Americans from leaving their current jobs to try and start a small business. If you have diabetes, heart disease, cancer, or any number of other conditions, it is impossible to buy individual health insurance. As a result, millions of potential small business owners are economically trapped in their current jobs.
Most importantly, the American people want health care reform. The vast majority of voters are worried about the cost of health care, and 60% of them voted for Barack Obama. Health care is not only a winning issue for Democrats, but also a great issue to raise money off of. Republicans have talked about blocking the Democrats' plans but have yet to put forth a good alternative of their own. It would be a mistake leave the Democrats with such a potent issue to bash them with for another election cycle.