Republicans who have taken over state capitols across the country are promising to respond to crippling budget deficits with an array of cuts, among them proposals to reduce public workers’ benefits in Wisconsin, scale back social services in Maine and sell off state liquor stores in Pennsylvania, endangering the jobs of thousands of state workers.

States face huge deficits, even after several grueling years of them, and just as billions of dollars in stimulus money from Washington is drying up.

With some of these new Republican state leaders having taken the possibility of tax increases off the table in their campaigns, deep cuts in state spending will be needed. These leaders, committed to smaller government, say that is the idea.

“We’re going to do what families and businesses all over this country have already had to do, and that is live within their means,” said Brian Bosma, a Republican who will soon become the speaker of the Indiana House, alongside a Republican governor, Mitch Daniels, and a supermajority of Republicans in the state Senate.

In that state, Bosma said, 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. 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.

As for public employees’ wages and benefits, Walker said he hoped to force them “into line” with everyone else’s.

“Public employees can’t be haves, while private sector employees are have-nots,” he said.

In Pennsylvania, a state not fully controlled by Republicans since 2002, Gov.-elect Tom Corbett must consider both a budget gap that could run as high as $5 billion and his campaign pledge not to raise taxes.

Among the steps Republican leaders there are pondering: privatizing the state’s 600-plus liquor stores, a proposal that would potentially bring $2 billion for state coffers, but also layoffs of several thousand state workers.

“That moved up to the top of the agenda,” Dominic Pileggi, the state Senate majority leader, said of the notion, which had been batted around for years but had faded under Edward G. Rendell, the departing Democratic governor.

Elsewhere, state leaders are expected to consider privatizing services now carried out by public employees as part of their broader examinations of the costs and size of government.

Other cost-cutting measures Corbett has talked about include slashing the fleet of roughly 16,000 state vehicles and taking away certain perks from lawmakers, like per diem payments.

State workers, education leaders and social services agencies are bracing. Since last week, some have met in various states to prepare counterattacks against what Terry W. Hartle, of the American Council of Education, which represents leaders of colleges and universities, described as the “eye-popping” level of “draconian” cuts it would take to balance some state budgets without new revenues.

To solve deficits in the last few years, many states have already made drastic cuts as well as raising taxes (half the states raised taxes in 2009, netting more than $28 billion, according to the National Conference of State Legislatures). And while there are signs that state revenues may be starting to improve, in most places they are not expected to return to pre-recession levels for a while.

Some Democrats, like B. Patrick Bauer, the departing Democratic speaker of the Indiana House, say they fear what some of the proposals — like one in Indiana to cut unemployment benefits, create an automatic refund mechanism for taxpayers if state reserves reach a certain level, and shrink the size of government — may ultimately mean for poor people, working people and sick people.

“They ought to all be worried,” Bauer said.

Meanwhile, opponents of the Obama administration’s health care law, business leaders, and conservative groups have begun making plans, too, for what they expect will be a series of welcome openings. Among the possibilities: a new flurry of proposed state prohibitions on abortion, same-sex marriage and illegal immigration.

“I feel like a little boy on Christmas morning — which package do you open up first?” Troy Newman, the leader of Operation Rescue, an anti-abortion group.

Already, abortion opponents were considering pressing for new regulations in New Mexico, Iowa and Kansas, where Sam Brownback, the Republican governor-elect, follows Democratic governors who vetoed some abortion limits approved by the Republican legislature.

For some states, like Arizona, Georgia, North Dakota and Texas, Republican domination in state capitals is not new (though in each of those, the size of Republican margins in legislatures grew in last week’s election). And at least four states, including California, Hawaii and Vermont, shifted to one-party Democratic control.

But the larger pattern was Republican, a trend lawmakers said would affect the policy conversation even in states with divided governments.

Issues now likely to come to a debate in New Mexico, for instance, where Republicans won the governorship and made major gains in the House, though Democrats maintained control of both the House and Senate: repeal of a law allowing drivers’ licenses for illegal immigrants and revocation of the licenses already issued; a requirement for photo identification cards at the polls; and the rollback of a 2008 environmental regulation dealing with the handling of waste from oil and gas operations

In many of these states, the new federal health care program is now certain to face new efforts to slow or stop it. Some of the newly elected governors have suggested joining a lawsuit, already supported by other states’ leaders, opposing it. Other leaders said they were weighing a series of options, including looking for ways to slow or steer clear of parts of the program (perhaps, the expansion of Medicaid or the creation of insurance exchanges), calling for a statewide referendum on the matter and lobbying their colleagues in Washington to force a repeal.

In Maine, where a remarkable political transformation occurred, creating a Republican-controlled state capital (an alignment not seen since the 1960s), there was an added possibility: In December, the state Legislature is to pick a secretary of state, treasurer and attorney general — the last of whom might play a role in the legal opposition to the health overhaul.

Paul LePage, the governor-elect there, also faces a projected $1 billion budget shortfall and has considered abolishing the state’s Land Use Regulation Commission, sending planning and licensing duties back to counties. Tarren Bragdon, a co-chairman of LePage’s transition team, said the new governor would probably also scale back the social safety net to focus on the “truly needy” in programs like food stamps, Medicaid and cash assistance, and look to remake the state’s health system.

That system, known as “Dirigo,” (Maine’s motto, which means “I lead” in Latin), was enacted several years ago in an effort to provide universal health care coverage for residents.

“Dirigo,” Bragdon said, “will be Diri-gone.”

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