WASHINGTON (AP) — House Speaker John Boehner said Thursday the "vast majority" of House Republicans believe they need to deal with immigration, but that they'll take a methodical, step-by-step approach and won't be held to any deadlines.

Legislation to secure the border and enforce immigration laws will come first, Boehner said. As for whether the House could ever agree to provide legal status or a path to citizenship for the 11 million immigrants already in the country illegally, "Well, we're going to find out," Boehner said.

"Through all the conversations that have occurred, with my own members, with Democrat members, it's clear that dealing with this in bite-sized chunks that members can digest and the American people can digest is the smartest way to go," said Boehner, R-Ohio. "And so I'm much more concerned about doing it right than I am in meeting some deadline."

The Ohio Republican spoke at a news conference Thursday, a day after House GOP members met to hash out their way forward on immigration.

They emerged with a consensus on dealing with border security first and moving legislation in pieces, in contrast to the sweeping bill passed last month by the Senate on a bipartisan 68 to 32 vote. What to do about the millions already here illegally remained unanswered.

With Democrats insisting on a path to citizenship, that left it unclear whether Congress will be able to get any kind of immigration bill to President Barack Obama's desk. The issue is one of the president's top second-term priorities.

At the White House Thursday Obama met with two of the lead authors of the Senate bill, Democrat Chuck Schumer of New York and Republican John McCain of Arizona.

Despite the uncertainty, Schumer and McCain both expressed optimism about where things stand in the House.

"The caucus sent out a message yesterday, which was the right message, which is, doing nothing is not an option," Schumer said.

Obama took a largely behind-the-scenes role as the bill moved through the Senate, and McCain suggested it could be a mistake for him to mount a more public campaign in support of immigration reform as the House takes it up.

"We want to be very careful that we have the president's participation but these members, these Republican House members — many of them are in districts that they will be representing for a long time — do not feel that they have been unduly pressured by the president of the United States," McCain said. "So I think the president is walking a careful line here, and I think it's the appropriate one."

It's not clear whether the House will take any action this month before Congress breaks in early August for its annual month-long summer recess. That would push the issue to the fall, when fiscal and other deadlines loom that could compete with immigration on the legislative calendar. If the issue is delayed until next year, the politics could become even trickier because it's a midterm election year when all House members will face voters.

Rep. Peter King of New York said that if any legislation came to the floor for a vote this month, it would deal only with border security.

Other lawmakers said even that approach raised concerns. Dealing with border security, they said, could lead to negotiations with the Senate that could morph into a compromise granting citizenship for some of the immigrants in the country illegally. They sought and received assurances from Boehner that he wouldn't let that happen, according to Rep. Kevin Cramer of North Dakota.

Boehner also said he won't put any bill on the House floor that doesn't have the support of at least half of the GOP rank and file, a pledge that only increases the challenge for Democrats and others who want to give a chance at citizenship to millions now in the country illegally

In explaining their piecemeal approach, Boehner and fellow GOP leaders said the administration's recent decision to postpone a key element of the health care law shows it can't be trusted to carry through on commitments, such as the one in the Senate immigration bill requiring the borders to be secured before anyone here illegally can get permanent resident status.

Unlike the comprehensive, bipartisan bill that cleared the Senate last month, the House Judiciary Committee has cleared four smaller measures in recent weeks, none of which would include the possibility of citizenship.

One would toughen enforcement of immigration laws and includes a provision that would permit local police officers to enforce such laws as part of an attempt to raise the number of deportations.

Other measures would create a new mandatory system for employees to verify the legal status of their workers, create a new temporary program for farm workers and expand the number of visas for employees in technology industries.

By contrast, the Senate bill would increase border security, provide a pathway to citizenship for many of the estimated 11 million immigrants illegally in the country, expand the highly skilled worker program and set up new guest worker arrangements for lower-skilled workers and farm laborers.