In Colorado, where Republicans are one seat away from control of the Senate, proposed limits on hydraulic fracturing could be curtailed. In the Nevada Senate, a Republican gain of one seat to take a majority could thwart the repeal of a constitutional ban on same-sex marriage. And if Republicans gain two seats to win control of the Iowa Senate, they are expected to push income- and corporate-tax cuts.

“Most of the key issues are taking place at the state level, and you’ll continue to see a clear course of action on the Republican side,” said Bill McCollum, chairman of the Republican State Leadership Committee and a former Florida congressman and attorney general.

Oregon, where the GOP needs two seats to gain a Senate majority, and Maine, where it needs three, are also high on the party’s target list. The more remote prospects on the party’s radar include the New Hampshire House, which has seen control flip three times in the past four elections; the Kentucky House; and both chambers in West Virginia, a state where President Barack Obama’s low approval ratings have created a particularly large burden for his party.

“Democrats are absolutely on the defensive in West Virginia,” Mr. Storey said.