Short answer is "no."
I can detect no signs that the Republican party has any better ideas for saving healthcare than the democrats. The problem is related to the lack of Phenomenologists in the political system. A phenomenologist would ask the question, "What is the essence of healthcare?" Of course, Aristotle would be asking the same question if he were alive today. To know a thing, one must know it's essence.
I submit that the essence of healthcare is appropriate treatment for illness or injury. Pretty simple and intuitive but the implication is profound for designing a well functioning and rational healthcare system.
There may be many paths that one could take to achieve appropriate care. I have suggested one model in this blog but acknowledge that there may be others. The key, it seems to me, is in the relationship between primary care and patients. If the primary care physicians have time and knowledge to properly diagnose and deliberately limit care to the clinical findings, we can approach a rational healthcare system. One of the keys is to pay primary care doctors promptly and fairly to reward a healthy patient/physician relationship. This is an area where short sighted insurance programs fail miserably.
Regardless of how we achieve appropriate care, the failure to do so will eventually bring down our healthcare system and and lead to rationing - either denial of service or failure to pay. As Pogo said, "We have met the enemy, and it is us."