The biggest obstacle Republicans face as they try and replace Obamacare is the fact that Republicans don't like anything that smacks of wealth transfer. A plan will not work for a big percent of the population and workers unless there is enough wealth transfer to provide subsidized premiums at the low end. Income inequality is just too wide, in USA, for universal access to health insurance without subsidy. This is a major stumbling block for Republicans.
Bringing overall healthcare costs down would help also. Part of the second solution is healthier lifestyles and diets. Politicians tend to not discuss that enough.
Reforming healthcare and the way insurance is handled can help also, but may be third on the list for solutions; in my opinion.
Main stumbling block for Republicans. The need for a subsidy.