Maybe they could take some of the heat off by passing a few less controversial measures to reduce the cost of healthcare. Remember the United States spends TWICE as much money on healthcare as any other country in the world. Perhaps bringing the costs down out of the stratosphere will ease things a bit. As it is, the Republican failure to deal with Obamacare will probably cost them control of Congress in 2018. Both houses.
They could try any or all of the following:
1. Allow interstate sale of health insurance. Any health insurance company can sell policies in all 50 states, no state paperwork required. Insurance companies hate this, but they don't vote.
2. Allow duty free import of drugs from any reasonable first world country, Canada, Britain, Germany, Japan, and the like. Any medicine legal for sale in the source country can be imported and sold in the United States. Drug companies hate this but they don't vote. The FDA hates this but they don't vote.
3. Clamp down on medical malpractice suits. They just enrich lawyers and make health care more expensive for real people. Lawyers (congresscritters are mostly lawyers) hate this. Unfortunately congresscritters do vote.
4. Ease the airconditioning requirements down from the current plus or minus 2 degrees F to a more reasonable plue or minus 4 degrees F. This will cut costs on new construction.
5. Tighten regulations on opioid prescriptions. Drug companies and pill mills hate this but they don't vote.
Granted, none of these measures will do any thing to prevent a bailout of insurance companies (stabilize is the new word for bailout), but at least the Republicans could say they did something about Obamacare.