WASHINGTON — A key Republican said Friday that President Barack Obama’s multibillion-dollar emergency request for the border is too big to get through the House, as a growing number of Democrats rejected policy changes Republicans are demanding as their price for approving any money.

The developments indicated that Obama faces an uphill climb as he pushes Congress to approve $3.7 billion to deal with tens of thousands of unaccompanied kids who’ve been arriving at the U.S.-Mexico border from poor and increasingly violent Central American nations. And they suggested that even as the children keep coming, any final resolution is likely weeks away on Capitol Hill.

As House members gathered Friday morning to finish up legislative business for the week, Rep. Hal Rogers of Kentucky, chairman of the Appropriations Committee, which controls spending, told reporters: “It’s too much money. We don’t need it.”

Rogers previously had sounded open to the spending request for more immigration judges, detention facilities, State Department programs and other items. He said his committee would look at the parts of Obama’s request that would go for immediate needs, but that others could be handled through Congress’ regular spending bills — though no final action is likely on those until after the November midterm elections.

And asked whether the House would approve the spending package as-is, Rogers said “no.”

White House Press Secretary Josh Earnest responded by saying that “we’re open to working with Democrats and Republicans in Congress to get this done.”

“The president has moved quickly to be very clear about what specifically needs to be funded,” Earnest said. “And we would like to see Republicans back up their rhetoric with the kind of urgent action that this situation merits.”

Rogers spoke shortly after the Congressional Hispanic Caucus convened a news conference to denounce efforts to attach legal changes to the spending measure that would result in returning the children home more quickly to El Salvador, Honduras and Guatemala. Those countries account for most of the more than 57,000 unaccompanied kids who’ve arrived since October.

Republicans are demanding such changes, and White House officials also have indicated support, while the House and Senate Democratic leaders left the door open to them this week.

But key Senate Democrats are opposed, and members of the all-Democratic Hispanic Caucus added their strong objections Friday that sending the children home quickly could put them at risk.

“I don’t know of a man or a woman in the Congressional Hispanic Caucus who is going to vote to undermine the rights of these children,” said Rep. Luis Gutierrez, D-Ill. “It would be unconscionable.”

Gutierrez said the lawmakers would make that same case directly to Obama in a meeting next week.

Meanwhile Homeland Security Secretary Jeh Johnson visited a detention facility in Artesia, New Mexico, where he said: “Our message to those who come illegally is we will send you back.”

That’s something that may not happen for years, if ever, under current circumstances, which is at the heart of the debate over changing U.S. policy.

At issue is a 2008 law aimed at helping victims of human trafficking, which appears to be contributing to the current crisis by ensuring court hearings for the children now arriving from Central America. In practice, that often allows them to stay in this country for years as their cases wend their way through the badly backlogged immigration court system, and oftentimes they never show up for their court dates.

Obama administration officials along with Republican lawmakers want to change the law so that Central American children can be treated the same way as Mexican minors, who can be turned around quickly by Border Patrol agents.

“If you want to stop the problem, treat the children humanely and send them back. I guarantee you it will work,” Senate Minority Leader Mitch McConnell, R-Ky., said Friday in a speech in Louisville.

Democrats and advocacy groups say such a change would put the kids in jeopardy.

“We will oppose this link even if it means the funding bill goes down,” said Kevin Appleby, director of migration and refugee policy for the U.S. Conference of Catholic Bishops. If the changes go through, “They’ll be sent back to their persecutors with no help whatsoever, and possibly to their deaths.”

The border controversy spilled over to a gathering of the National Governors Association in Nashville, Tennessee, where governors of both parties blamed a gridlocked Congress.

“Congress needs to act,” declared Oklahoma Gov. Mary Fallin, the group’s Republican chairman. “They are children, so we want to treat them very humanely, but we also have a lot of concerns for the health and wellness of our citizens in our state.”