House Speaker John Boehner dampened prospects for emergency action by Congress addressing the immigration crisis on the southern border before lawmakers break for their August recess.
"I don't have as much optimism as I'd like to have," Boehner told reporters on Thursday.
The Obama administration has warned that some federal agencies dealing with the surge of minors crossing the border, many of them unaccompanied, will run out of money sometime in August.
The House and Senate will return after Labor Day.
The major sticking point is whether Congress should change a 2008 law requiring that child migrants from Central America receive a hearing before any decision is made to deport them.
Critics say the Bush-era law has made the United States a magnet for children fleeing Guatemala, El Salvador, and Honduras.
They argue there should be an accelerated process to deport them, just like there is for children who enter the country illegally from Mexico or Canada.
Sen. John Cornyn and Democratic Rep Henry Cuellar, both of Texas, have introduced a bipartisan bill to modify the 2008 law and some version of their plan is expected to be attached to any House GOP package that includes emergency funding for border efforts.
But top Senate and House Democrats, and virtually all Hispanic lawmakers, are balking at the change.
House Democratic Leader Nancy Pelosi, who recently said she was open to accepting a change now opposes tying that to new funding.
Pelosi told reporters Thursday that any debate to reverse the law should be done separately, as part of comprehensive immigration reform.
President Barack Obama has proposed $3.7 billion in emergency funding to address the matter. He also does not advocate changing the 2008 law.
Boehner insisted, however, that that the law in question must be addressed.
"I don't know how Congress can send more money to the border to begin to mitigate the problem if don't do something about the '08 law that's being abused, and it is being abused," he said.
House GOP aides say Republicans are working on a package smaller than the one proposed by Obama with some policy changes. They expect to vote on it before the end of July.
Boehner's office said it has been involved in some bipartisan negotiations addressing the 2008 law.
Referencing her own shift in position, Pelosi said she never likes "to draw a line in the sand," noting that she was open "to seeing what's there" two weeks ago.
But now "what we've seen so far is going in the wrong direction and if they want Democratic votes it's got to go in the right direction," Pelosi said.
In the House, Boehner will need some Democratic support to pass a bill because there is a contingent of House conservatives who don't want to approve any more money for Obama administration's efforts.
If Pelosi and other top Democratic leaders stand firm, and Hispanic and progressive lawmakers vote no on a GOP package it could complicate getting something out of the House.
Over to the Senate
According to senior Senate Democratic sources, the caucus is fairly evenly divided between those who can accept proposed changes to the 2008 law in order to help speed passage of the funding and those who are unwilling to alter a law that was designed to provide due process to children who may be victims of crimes related to human trafficking.
Another wrinkle in the push to finalize a deal is a proposal from conservative Texas Republican Sen. Ted Cruz.
Cruz introduced legislation to prevent Obama from granting deportation deferments in the future. Obama signed an executive order two years ago allowing many young people who were brought to the United States illegally when they were children to stay.
Cruz said such acts of "amnesty" are deepening the current crisis by creating the impression that the children coming across the border now will eventually be allowed to stay.