House GOP leaders on Tuesday said they will insist that changes to a human trafficking law be included in any legislation responding to the wave of child immigrants crossing the border.

Republicans have blamed the influx of children at the border on the 2008 law, which they say has served as an incentive for people to enter the United States. The law allows minors entering the country from Central America, but not Mexico, to request asylum hearings.

President Obama has asked for $3.7 billion in emergency supplemental appropriations to care for people crossing the border, and to hire more judges and lawyers to send them back to their home countries more quickly.

The White House has separately asked for more authority to deport people, but has not provided specifics.

Democrats have expressed opposition to changing the trafficking law, which has emerged as a flashpoint in the political fight over what to do about the border crisis.

House Minority Whip Steny Hoyer (D-Md.) on Tuesday said Democrats would oppose changes to the 2008 law as a precondition for moving border funds, though he added he was open to a debate and hearings over the law.

Speaker John BoehnerJohn Andrew BoehnerJohn Feehery: A political forest fire Trump's pick for Federal Reserve chief is right choice at right time The two-party system is dying — let’s put it out of its misery MORE (R-Ohio) said at the weekly House GOP press conference that a final decision on legislation would likely come by the end of the week.

In the meantime, BoehnerJohn Andrew BoehnerJohn Feehery: A political forest fire Trump's pick for Federal Reserve chief is right choice at right time The two-party system is dying — let’s put it out of its misery MORE said, the GOP was still awaiting final recommendations from the House Appropriations Committee and a border working group led by Rep. Kay GrangerNorvell (Kay) Kay GrangerSeven Texas lawmakers leaving Congress means a younger, more diverse delegation House passes .5 billion disaster relief package GOP lawmaker: No town halls because of threats against lawmakers MORE (R-Texas). Her group presented its initial findings to the conference on Tuesday.

It is not clear whether House Republicans will push for a smaller price tag for the appropriations package.

House Appropriations Committee Chairman Hal Rogers (R-Ky.) said he was waiting on the final recommendations from Granger’s group before figuring out how much it would all cost. He added that his team will also be trying to figure out how much of the administration’s $3.7 billion request is needed immediately, and what could be dealt with during the regular appropriations process.

“I want a chance to see what they’re recommending, because some of these items could relate to how much money we have to spend. We’ll wait and see what the recommendations are,” Rogers told reporters. “We’ve got a regular process going on now ... if the money’s not needed now, they can be looked at in the regular process.”

Rep. Henry Cuellar (D-Texas) and Sen. John CornynJohn CornynMcConnell names Senate GOP tax conferees Air Force makes criminal reporting changes after Texas massacre We need a better pathway for allowing civilians to move guns across state lines MORE (R-Texas) have introduced legislation to amend a 2008 trafficking law so that all child immigrants crossing the border undergo the same process, regardless of where they come from.

"I think it would be an element of anything we do," said House Majority Leader-elect Kevin McCarthy (R-Calif.).

Granger said she would be releasing a formal set of recommendations later Tuesday or Wednesday morning. That group also backs changing the 2008 law, and wants to send National Guard troops to the border.

Rep. Matt SalmonMatt SalmonMcSally tells GOP colleagues she'll run for Arizona Senate GOP Senate hopeful Kelli Ward leads challengers in internal poll Paul says he still supports McConnell after endorsing anti-McConnell candidate MORE (R-Ariz.), a member of the working group who traveled to Honduras and Guatemala over the weekend, said the final review from the group and the House Appropriations Committee later in the week would be combined and possibly yield other demands.

"Right now, this group is working on policy, while Appropriations Committee Chairman Rogers is working on the funding," Salmon said. "Once you marry those things, there may be some changes along the way."

Members of Granger’s working group left Tuesday’s meeting with House Republicans for a meeting with Homeland Security Secretary Jeh Johnson, hours before they were set to release their formal recommendations.

Updated at 12:08.

Timothy Cama contributed.