(CNN) -

House Republicans are making it clear there won't be a speedy vote on President Barack Obama's $3.7 billion emergency proposal to address the immigration crisis on the southern border.

They believe less money is needed and more should be done to strengthen enforcement along the border, which has experienced an unexpected surge of children from Central America. Many of them are unaccompanied.

House Speaker John Boehner, speaking to reporters on Wednesday after a closed-door meeting with House Republicans, didn't say what the GOP would propose. But he criticized Obama for not already taking action under current law.

"If we don't secure the border, nothing is going to change. If you look at the President's request, it's all more about continuing to deal with the problem. We've got to do something about sealing the border and ending this problem so that we can begin to move onto the bigger questions of immigration reform," Boehner said.

He said the House Appropriations Committee and a working group he assembled last month were reviewing the $3.7 billion package Obama proposed to a deeply divided Congress.

He urged on Wednesday during a visit to Texas that lawmakers put aside politics and swiftly approve the plan that seeks to bolster customs and border efforts as well as crack down on smugglers. Another goal is to speed the processing of young immigrants and send back those who lack legal status. Money would also go to caring for unaccompanied children.

The working group is meeting on Wednesday and is scheduled to deliver recommendations to Boehner next Tuesday.

One member of the group, Florida Republican Mario Diaz-Balart, believes they will quickly come up with proposals.

"The answer is not just necessarily to throw more money at it," he told reporters.

While more resources may be needed for targeted purposes, Diaz-Balart said "the House is never going to rubber stamp what the President wants to do. But I think there is a realization that there is a crisis."

House Homeland Security Chairman Michael McCaul and other House GOP members want to change a 2008 law signed by President George W. Bush requiring deportation hearings before sending back unaccompanied children from countries that do not border the United States. The measure was aimed at combating illegal trafficking.

A GOP proposal to do so will be made on Thursday by Rep. Henry Cuellar, whose South Texas district is one heavily impacted by the current crisis, and Texas Sen. John Cornyn.

Many GOP lawmakers argue all minors should be treated like children who enter the country from Mexico and Canada -- they are returned immediately.

But California Democrat Zoe Lofgren suggested the problem is not the law, but a lack of judges to handle cases.

Just back from a border detention center housing immigrant children temporarily, Lofgren said they are being identified and processed under existing law.

But "we don't have the resources to do this properly, and we should do that. And I think if we adhere to the law I think we're going to be satisfied with the results," she said.

Although it's unclear how much of Obama's proposal would survive in Congress, Boehner told Republicans the House would take some action on immigration before it leaves for a month-long recess in August, according to two GOP sources who attended the meeting.