Mr. Bosma said state revenues next year are expected to reach only the levels of about five years ago, creating an enormous strain. “We’re going to do what is right, and we’ll let the politics land where they may,” he said.

All sorts of candidates make all sorts of promises along campaign trails, but there is a difference after last week’s election: in many states, Republicans have gained such control that when they take office in the coming months they will have a much easier time carrying out whatever agenda they choose.

In some cases, that may mean not just greatly changing state policies on taxing and spending, but also loosening regulations facing businesses, restricting access to abortion and rights for illegal immigration, and, perhaps, slowing the Obama administration’s health care overhaul.

Republicans gained more than 690 seats in state legislatures (leaving them with numbers last seen more than 80 years ago), at least five more governor seats, and, perhaps most significant, across-the-board power in the legislatures and governor’s offices of at least 20 states  more than twice as many as before the election. Included in that group were Maine and Wisconsin, which the day before the election had been entirely in Democratic hands.

“It’s kind of put up or shut up time,“ said Scott Walker, the governor-elect of Wisconsin, which experienced the largest flip in power in memory. Mr. Walker, a Republican, said he intended to navigate a projected $3 billion budget gap with no tax increases. He also said he planned to remove all “litigation, regulation, excessive cost“ barriers to businesses (declaring Wisconsin, on election night, “open for business!”), and to put an end to a plan for a federally financed rail project between Milwaukee and Madison that he says would cost too much for the state to operate once it is built.