Republicans in statehouses across the country are plotting a tough new campaign to check the power of labor unions and chip away at their political influence.

The GOP lawmakers, buoyed by sweeping midterm victories at the state level, are weighing so-called "right-to-work" bills in several capitals once new legislative sessions start in January. The measures, already in place in two-dozen states, generally prohibit unions from forcing workers in the private sector to join and pay dues.

"The accumulated gains by Republicans in state legislatures will certainly increase pressure on, and within, the GOP caucuses to expand right-to-work laws," Louis Jacobson, state politics columnist for Governing magazine, told FoxNews.com.

Wisconsin and Ohio are considered among the mostly likely to back the legislation, as Republicans control both chambers of those legislatures and the governorships -- though those governors seem lukewarm to the idea. Colorado, Missouri, New Hampshire and New Mexico also could see battles over union power next year.

Once again, Wisconsin is expected to be at the forefront of the union drama.

Republican state Rep. Chris Kapenga plans to propose a right-to-work bill for private-sector workers. And state Sen. Scott Fitzgerald, the Senate majority leader, claims his chamber will act quickly to pass such legislation. Gov. Scott Walker, though, repeatedly has suggested he doesn't want the legislature to tackle the issue right now.

"As he has said previously, Gov. Walker's focus is on growing Wisconsin's economy and creating jobs," spokeswoman Laurel Patrick recently said. "Anything that distracts from that is not a priority for him."

The stance might seem unusual for Walker.

In 2011, he pushed a law through the legislature that effectively ended collective bargaining for most public-sector workers and included right-to-work language for those workers. Walker's move -- prompting weeks of massive protests and a failed recall effort -- raised his national profile to the point that he's considering a run for president.

But with a 2016 decision looming, he likely wants to avoid another potentially extended and perilous state-level fight, Marquette Law School professor Paul Secunda said.

Kapenga told FoxNews.com that he and others are working on the union legislation but declined to speculate on what Walker might be thinking.

"I don't want to put words in his mouth," he said. "My job is to lay out a compelling case. But I plan to sit down with him."

Meanwhile, big labor is gearing up for a battle.

"We'll fight this every step of the way," said Phil Neuenfeldt, president of the Wisconsin AFL-CIO. The private-sector union also is reportedly planning similar efforts in other states.

Twenty-four states already have right-to-work laws, including Michigan and Indiana.

Supporters say the laws give workers more freedom since they aren't required to join unions or have dues deducted and argue such laws help attract businesses.

Opponents -- including Democrats and the labor unions that often support Democratic candidates -- argue the laws are bad for workers, hurt the economy and are designed to weaken union power and political clout.

Both sides likely would agree the battle would impact a relatively small and dwindling percentage of workers.

Roughly just 11.3 percent of private- and public-sector workers were members of unions last year, based on U.S. Bureau of Labor Statistics figures. The number is down from 20.1 percent in 1983 and a record high of nearly 35 percent in 1954.

In Ohio, right-to-work legislation died without a vote this year and failed in a 2011 referendum that was backed by GOP Gov. John Kasich.

The issue is expected to resurface in 2015. But Kasich, who won reelection this fall, has not said whether he would sign such legislation.

He told a Gannett newspaper editorial board in September that companies appear willing to come to Ohio despite no right-to-work laws.

However, political observers suggest Kasich, who during his first term presided over an improving state economy, didn't want to jeopardize that success or his reelection bid by alienating pro-union voters and others.

Jacobson said that while GOP state lawmakers may move toward pressuring the unions, "in 'purple' states, the governors may feel pressure to quietly downplay such efforts, especially if they have aspirations for national office."

In New Mexico, Democrats have control of the state Senate. But in November, Republicans won the House majority, which could give them their best opportunity in decades to pass such a bill.

"This time could be the time we get it through both houses," Senate Minority Leader Stuart Ingle, a Republican, said just days after the Nov. 4 election.

GOP Gov. Susana Martinez appears to support right-to-work legislation. But she did not make the legislation a big part of her successful re-election campaign, and whether she would sign such a bill remains unclear.

In Missouri, the measure narrowly failed last year. But Republicans this fall added to their two-thirds-plus majority in both legislative chambers, which means they would be able to override vetoes by Democratic Gov. Jay Nixon.

In New Hampshire -- where a right-to-work bill died earlier this year -- a Democrat kept the governor's seat, but Republicans won control of the state House and maintained control of the Senate.

Republicans also passed such a bill in 2011 when they controlled both chambers, but it was vetoed by then-Gov. John Lynch, a Democrat.

FoxNews.com's Joseph Weber and The Associated Press contributed to this report.