“The American people are skeptical of big, comprehensive bills, and frankly, they should be,” Mr. Boehner told reporters recently. “The only way to make sure immigration reform works this time is to address these complicated issues one step at a time. I think doing so will give the American people confidence that we’re dealing with these issues in a thoughtful way and a deliberative way.”

Nonetheless, immigration activists say they are hopeful that politics may ultimately lead Mr. Boehner to ignore conservative voices who oppose a path to citizenship. Mitt Romney, the Republican nominee for president in 2012, who took a hard line on immigration, won only 27 percent of the Hispanic vote — a key reason for his loss to President Obama.

Mr. Obama has in the meantime said he is open to the piecemeal approach on immigration favored by House Republicans, but only if it does not abandon comprehensive goals in legislation that passed the Senate last summer. Reconciling the House approach with the broader ambitions of the Senate bill is the biggest hurdle, strategists in both camps say.

“We’ve got to grab the brass ring while it’s there,” said Kevin Appleby, the director of migration policy at the United States Conference of Catholic Bishops. “I’ve been in this debate long enough to know you can’t rely on anything happening at a certain time or on assurances that we’re going to do something this year.”

Advocates for an immigration overhaul will start 2014 with a race against the election-season clock and a new campaign aimed at forcing action on Capitol Hill. Civil disobedience demonstrations are planned in Washington and elsewhere. Business groups are readying lobbying blitzes on Capitol Hill. Labor leaders and evangelical ministers are considering more hunger fasts to dramatize what they say is the urgent need to prevent deportations.

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.”