House Speaker John A. Boehner (R-Ohio), joined at right by incoming Majority Leader Kevin McCarthy (R-Calif.), talks with reporters Wednesday following a Republican strategy session. (J. Scott Applewhite/Associated Press)

A House Republican plan to address the influx of illegal immigrants at the U.S.-Mexico border would cost considerably less than President Obama has requested but could get upended by the political forces that long have divided GOP lawmakers.

The $1.5 billion proposal unveiled Wednesday proposes to spend far less than Obama’s
$3.7 billion request to provide more resources along the southern border and to care for the record number of migrants who have arrived in recent months. It would mandate the deployment of National Guard troops, boost funding for Border Patrol, and require the administration to more quickly process and deport young children and families who have illegally entered the country.

But it was unclear how rapidly the House could advance the proposal and whether House Republicans will be able to reach agreement with Senate Democrats on a final deal before Congress adjourns Aug. 1 for a five-week recess.

“I’d like to act. We’ve got a humanitarian crisis on the border that has to be dealt with,” House Speaker John A. Boehner (R-Ohio) told reporters Wednesday. But Boehner also faulted Obama for failing to work with Congress to swiftly seek a solution.

“The administration ought to get their act together,” he said. Later, Boehner’s office sent a letter to the White House asking for clarification on whether it supports changing a 2008 ­anti-trafficking law to make it easier to deport minors from Central America.

That issue remains central to the impasse.

The Obama administration informed Congress in a letter this month that it was seeking greater authority for the Homeland Security secretary to deport the Central American minors quickly. But faced with strenuous opposition from leading Democrats and immigrant-rights groups, the White House did not suggest legislative language to make the change in its emergency funding request. Administration officials continue to say they would support efforts to amend the law but have not suggested specific changes.

In the Senate, Democrats plan to move forward on a spending bill to provide $2.7 billion in emergency funds to deal with the influx of minors — about $1 billion less than Obama’s request. The Democratic plan will not include amendments to the 2008 law.

In the House, Rep. Kay Granger (R-Tex.), who led the House GOP’s working group tasked with tackling the issue, shared her team’s recommendations during the weekly closed-door meeting of House Republicans. On her way into that meeting, Granger said a vote on her proposals “should happen right now.

“Every day that we delay, thousands more come across the border,” she said.

Granger said her proposals would tweak the 2008 law, but not repeal it.

The changes, she said, would “change a portion that will let us send the children back in a very speedy way.”

Dangerous journeys taken by unaccompanied children

An hour before Granger addressed her colleagues, Sen. Ted Cruz (R-Texas), a favorite of tea party activists, met with more than a dozen House Republicans over a breakfast of Chick-fil-A items and coffee. He urged them to not buckle to Democratic demands for compromise on the scope and cost of legislation.

Cruz spoke at a meeting of the Conservative Opportunity Society at the invitation of the group’s chairman, Rep. Steve King ­(R-Iowa), a prominent critic of bipartisan efforts to pass comprehensive immigration reform.

“He’s a perfect catalyst and he has a real rapport with conservatives in the House,” King said in an interview. “He really wanted to hear from people in the room. He also let us know that anything we send to the Senate, if it comes back, it’s going to be terrible, so we should make sure we’re ready to respond to that.”

King said that he and many others there are likely to oppose the initial GOP House plan.

“I’m leaning no. The Granger report is constructive, but no one has come up with a plan for how to deal with the Senate,” King said. “We’re putting our head in the noose and associating ourselves with the president’s problem.”

Cruz said that Granger’s plan includes “a number of good and positive elements.” But he added that other Obama policies are to blame for the uptick in illegal immigrants.

Other Republicans said Wednesday that they want to act quickly.

“People want to be able to go home and say, ‘we’ve done something.’ And what we’re doing is eminently defensible,” said Rep. Tom Cole (R-Okla.), a Boehner ally. “We’re putting an offer on the table and waiting to see what the Senate does. If we didn’t act, it would play right into the president’s hands.”

In order to pay for the changes, Rep. Harold Rogers (R-Ky.), who chairs the House Appropriations Committee, said that about half of the $1.5 billion would pay for National Guard deployments and to bolster the Border Patrol. About one-third of the money would be provided to the Department of Health and Human Services for the ongoing housing and care of migrants, far below the $1.8 billion requested by Obama.

With Congress still mulling what to do, the presidents of El Salvador, Guatemala and Honduras are scheduled to visit Capitol Hill on Thursday to appeal directly to lawmakers for assistance. They will meet with Obama at the White House on Friday.

David Nakamura contributed to this report.