A year after a coterie of new Republican governors swept into the statehouses and put in place aggressive agendas to cut spending and curb union powers, sparking strong backlashes in many places, many of them are adopting decidedly more moderate tones as they begin their sophomore year in office.

The efforts to weaken unions have not ended — witness the recent events in Indianapolis, where the longtime Republican governor, Mitch Daniels, supports making Indiana the first state in the industrial Midwest with so-called right-to-work legislation. But many of the new Republican governors who swept into office last year, taking aim at collective bargaining rights, are striking less confrontational notes as they begin the new year, at least judging by what they have been saying in their State of the State addresses.

A gradually improving economy has eased some of the pressure for steep spending cuts. Many state lawmakers face re-election this year, and in many states they are showing little appetite to face the kind of uproar that greeted efforts to curb collective bargaining rights in states like Ohio and Wisconsin last year. And with a presidential campaign unfolding, some Republicans worry that overreaching at the local level, particularly in swing states, would make it harder for them to win in November.

No state had more tumult last year than Wisconsin. Its governor, Scott Walker, a Republican, signed a law to curb collective bargaining rights for public workers, sparking protests and sit-ins at the State Capitol and now a campaign to have him recalled from office.

While he used his State of the State speech on Wednesday to defend the unpopular measures he took last year — telling lawmakers that "we thought more about the next generation than we did about the next election" — the agenda he sketched out for this year was far less controversial. Among its highlights: a call for a law to bring more mining to the state, a task force to eliminate government waste and a literacy program.

In Florida, Gov. Rick Scott, a Republican who was elected in 2010 with the support of the Tea Party movement, has a new priority this year: He wants lawmakers to restore $1 billion of the roughly $1.35 billion in education cuts that he pushed through last year. "On this point, I just cannot budge," he said in his second State of the State address.

And there was a different atmosphere on display last week in Maine. Its governor, Paul R. LePage, a Republican with Tea Party support, ruffled feathers last year by sparring with the NAACP over his decision to skip an event on Martin Luther King’s birthday, ordering the removal of a mural at the state’s Department of Labor that he complained was too pro-labor and cutting taxes while calling for cuts in social programs for the poor.

While LePage used his speech last week to renew his calls to cut welfare spending, he did reach out to Democrats near the end. Noting that he had been a victim of domestic violence as a child, LePage made an emotional appeal to strengthen the state’s domestic violence laws, and he thanked the Democratic minority leader in the state’s House of Representatives, Emily Ann Cain, by name for offering to sponsor one of the bills.

"Now Emily — my tone alright?" the governor asked Cain, departing from his prepared text.

"You’re awesome!" she replied with a smile, giving him the thumbs up.

To be sure, some governors — both first-termers and veterans — are still proposing measures that are sure to kick up a fuss this year.

Gov. Sam Brownback of Kansas, a Republican, proposed a major overhaul of the state’s tax system that would lower tax rates but eliminate deductions and credits — including popular ones, like deductions for mortgage interest and charitable contributions and tax credits for poor families. His proposal is similar to one made in Washington in 2010 by President Barack Obama’s deficit reduction commission, but quickly shot down. Some Republican lawmakers in Kansas are balking at the idea of ending the deductions and credits.

And more laws that aim to curb the power of unions are being pursued in a number of states this year.

Unions and Democrats were thrown on the defensive this year in Indiana when Daniels, serving in his second — and last — term, switched course and decided to support a bill to ban union contracts from requiring nonunion members to pay union dues.

Last year Daniels, who was considering a run for president, told lawmakers that such legislation was so divisive that it could derail the rest of his legislative agenda. But this year he decided that the measure, which supporters call a right-to-work law, would attract more jobs to Indiana.

"The idea, that no worker should be forced to pay union dues as a condition of keeping a job, is simple, and just," Daniels said in his State of the State address. "But the benefits in new jobs would be large: a third or more of growing or relocating businesses will not consider a state that does not provide workers this protection."

In South Carolina, a right-to-work state whose unemployment rate remained at 9.5 percent in December, above the national average, Gov. Nikki R. Haley, a Republican beginning her second year in office, took a hard line on unions in her address to the Legislature.

"I love that we are one of the least unionized states in the country," she said, calling it "an economic development tool unlike any other." She pledged to "make the unions understand full well that they are not needed, not wanted and not welcome in the state of South Carolina."

Teacher tenure continues to be a flashpoint in many states. The governors of New Jersey, South Dakota and Virginia all used their speeches this year to call for abolishing or weakening it — following the path that an unusually large number of states took over the last year. Gov. Chris Christie of New Jersey said, "We cannot ask parents to accept failure in teachers when their children’s lives hang in the balance."

There are now Republican governors in 29 states, Democratic governors in 20, and one independent, in Rhode Island. Governors in both parties used their State of the State addresses to argue that some of the hard choices they have been forced to make in recent years, as states faced record deficits, had put their states on a path to stability. Several, including Gov. Jerry Brown of California, a Democrat, used their speeches to call for finding ways to cut pension costs.

Of course, governors do not always propose their toughest measures in their annual speeches to lawmakers. Last year, Walker of Wisconsin used his State of the State address to call on government workers to contribute more to their pension plans; he did not mention his plan to curb collective bargaining rights until later.

As the economy has slowly improved, state tax revenues have been steadily rebounding. A report last week by the Nelson A. Rockefeller Institute of Government found that state tax collections in the third quarter of 2011 were only 1.2 percent lower than they were in the same quarter of 2008.

But states still face short-term challenges and enormous long-term liabilities, and Standard & Poor’s cautioned last week that "compared to when the recession began, state and local governments have fewer tools in their fiscal tool boxes."

Still, many governors are moving to undo, or at least soften, some of the measures they took during the downturn.

In Arizona that means buying back the state’s Capitol complex, which was sold after the housing meltdown sent the state into a downward spiral. Gov. Jan Brewer, a Republican, used her State of the State address this year to urge legislation allowing her to buy it back. "Together, we can celebrate the burning of that mortgage!" she said.

And in Georgia, Gov. Nathan Deal, a Republican, called for restoring half of the days of prekindergarten classes that he cut last year to save money.

Mostly, though, governors sounded pleased to have simply survived the fiscal tumult of recent years. "When I took office, the state had just ended the last fiscal year with only $876 in the state general fund," Brownback of Kansas said, echoing the kind of war story many governors have. "Excuse me, 876 dollars and 5 cents."