The most divisive of the points is a proposed pathway to legal status for millions of adults who live in the U.S. unlawfully and would be required to pay back taxes as well as fines to come out of the legal shadows. The principles also include steps to increase security at the nation's borders and workplaces.
As contentious as it is, the proposal for legal status falls short of full citizenship, which was included in a bipartisan measure that cleared the Senate last year with the support of President Barack Obama.
The entire subject remains intensely controversial, particularly among conservatives in the House and Senate.
Rep. Steve Scalise, R-La., who heads the Republican Study Conference, a group of conservative lawmakers, repeatedly declined to say whether there are any circumstances under which he would be able to support legislation that bestowed legal status on adults currently living in the country illegally.
Another Republican, Rep. Jason Smith of Missouri, told reporters that his constituents "definitely have big concerns about legalization."
The drive to overhaul immigration laws flagged after the Senate acted, as House conservatives dug in. The House Judiciary Committee has approved four bills, but none has reached the House floor as conservatives have expressed concern about being drawn into an eventual compromise with the White House.
One of those bills would toughen enforcement of immigration laws, including a provision that would permit local police officers to enforce them as part of an attempt to raise the number of deportations. It also would encourage immigrants in the United States illegally to depart voluntarily, an echo of Mitt Romney's call for "self-deportation" in the 2012 presidential race.
Other measures would create a new system for requiring employees to verify the legal status of their workers, establish a new temporary program for farm workers and expand the number of visas for employees in technology industries.
The political drive for immigration legislation among Republicans stems from the party's abysmal showing in recent elections among Hispanic voters.
Yet many conservative House members are from congressional districts with relatively few Hispanic residents, and they have more to fear politically from a challenge from the right. Additionally, current polls suggest Republicans are well-positioned to retain control of the House and perhaps gain a Senate majority as well, so some strategists see even less reason for compromise on the issue than before.
As the House Republicans gathered, a prominent opponent of the Senate bill, Sen. Jeff Sessions, R-Ala, circulated a detailed point-by-point rebuttal to the proposal that Boehner and the leadership have prepared.
Congress "must end lawlessness, not surrender to it," he said.
Boehner is moving carefully after failing a year ago to persuade the Republican rank and file to support an overhaul.
"It's time to deal with it, but how you deal with it is critically important," he said at a news conference Thursday.
It's one thing to pass a law, it's another thing to have the confidence of the American people behind the law, he said.
Numerous Republicans told reporters they wanted the party to be seen as offering alternatives to Obama this year rather than simply opposing him.
Aside from the immigration question, several said they favor drafting health care legislation for floor debate. Republicans campaigned as vigorous opponents of "Obamacare" when they won power in 2010, vowing to "repeal and replace" the law.
Three years later, they have voted more than 40 times to repeal or eviscerate the law, and they triggered a partial government shutdown last year in a failed attempt to defund it. But they have yet to produce an alternative, and some strategists argue the law is so unpopular that it would be a mistake to do so.
Rep. Greg Walden, who chairs the GOP campaign committee, said he does not share that view.
"If we're just seen as the opposition party, we miss a great opportunity," he said.
Republicans were emphatic about several measures as they met.
Boehner challenged Obama to override objections from the Senate's top Democrat, Majority Leader Harry Reid of Nevada, and work to pass trade promotion legislation that the president called for in his State of the Union address.
House GOP leaders also sent a letter to Obama urging him to help pass legislation that covers several other areas he mentioned in the speech. House-passed measures on the topics are bottled up in the Democratic-controlled Senate.