Through the use of mandatory health savings accounts, Singapore's health care system makes better use of the price system than the American health care system, which Republicans should like. This makes it cost less than the American system, while providing Singaporeans with better overall health than Americans.
From the libertarian EconLog blog:
The Singapore government spent only 1.3 percent of GDP on healthcare in 2002, whereas the combined public and private expenditure on healthcare amounted to a low 4.3 percent of GDP. By contrast, the United States spent 14.6 percent of its GDP on healthcare that year, up from 7 percent in 1970... Yet, indicators such as infant mortality rates or years of average healthy life expectancy are slightly more favorable in Singapore than in the United States... It is true that such indicators are also related to the overall living environment and not only to healthcare spending. Nonetheless, international experts rank Singapore's healthcare system among the most successful in the world in terms of cost-effectiveness and community health results.
For more info on Singapore's health care system, read here, here, here, and here.