Republicans’ consolidation of power in state capitols is likely to expand the number of states that employ a far more limited, free-market-oriented approach to implementing the nation’s new health-care law than the robust regulatory model favored by its supporters.

Although the law is a federal statute, it tasks states with administering many of its most important provisions and grants them considerable leeway.

It is up to states to run markets, known as “exchanges,” through which individuals and small businesses will be able to buy health insurance plans, often with federal subsidies, beginning in 2014…

The result, analysts say, is that two models are likely to appear: Democratic governors and legislatures are likely to emphasize vigorous regulation and government oversight, while Republican state leaders are likely to put greater stock in privatization and other free-market approaches.