WASHINGTON — Speaker John A. Boehner of Ohio has signaled he may embrace a series of limited changes to the nation’s immigration laws in the coming months, giving advocates for change new hope that 2014 might be the year that a bitterly divided Congress reaches a political compromise to overhaul the sprawling system.

Mr. Boehner has in recent weeks hired Rebecca Tallent, a longtime immigration adviser to Senator John McCain, the Arizona Republican who has long backed broad immigration changes. Advocates for an overhaul say the hiring, as well as angry comments by Mr. Boehner critical of Tea Party opposition to the recent budget deal in Congress, indicates that he is serious about revamping the immigration system despite deep reservations from conservative Republicans….

The most likely legislative approach, according to lawmakers, White House officials and activists, is a push to pass legislation in the House by May or June — after most Republican lawmakers are through with their primary campaigns — with the goal of reaching a compromise that Mr. Obama could sign before the 2014 midterm election campaigns intensify next fall.

“That’s our first window,” said Jim Wallis, the president of Sojourners, a Christian social justice organization in Washington that is working to change the immigration laws. “We are organizing, mobilizing, getting ready here. I do really think that we have a real chance at this in the first half of the year.”

If a comprehensive overhaul is not completed by summer, strategists say they could make another push during a lame-duck session at the end of the year, after the November elections. If it did not happen then, lawmakers could wait until 2015, although advocates would have to start again in the Senate because the legislation would expire at the end of 2014.