House Republican leaders are trying anew to round up an elusive majority for a bill addressing the border crisis, after a chaotic day where they initially abandoned the legislation and began sending lawmakers home for the summer recess -- only to reverse course moments later.

The dramatic scene unfolded at a rapid clip Thursday afternoon. Earlier, House leaders abruptly canceled a planned vote on a package meant to address the surge of illegal immigrant minors crossing the U.S.-Mexico border, with a combination of funding and policy changes, after failing to gather enough votes for it.

Lawmakers began heading out for the five-week summer recess. But incoming House Majority Leader Kevin McCarthy, R-Calif., then took to the floor to say "additional votes are possible," indicating lawmakers should stay. Boos could be heard in the House chamber as he made the announcement.

But House Republicans later huddled on Capitol Hill before the House adjourned for the day. It was scheduled to meet again Friday morning.

Meanwhile, a different piece of border legislation died Thursday night in the Senate on a procedural vote. So even if the House did succeed in passing a bill Friday, there was no prospect for reaching a deal to send a bill to Obama's desk.

More On This...

The second thoughts in the House reflected deep concerns in the GOP caucus about the prospect of leaving for the August recess without addressing the border bill, amid criticism from both sides of the aisle.

It remains unclear whether there's any chance enough votes can be rounded up to pass the measure. Senior Republican leaders were adamant, though, that something must be done, regardless of the looming recess.

"We'll stay until we vote," House oversight committee Chairman Darrell Issa, R-Calif., said.

Asked if the House can find a solution, House Energy and Commerce Committee Chairman Fred Upton, R-Mich., said: "We'd better."

If lawmakers do end up breaking for recess without a bill, House leaders left open the possibility of recalling members if need be when they feel they have a majority of 218 votes. Earlier, sources said GOP leaders were "way short" of the votes they needed, with conservative lawmakers joining Democrats in refusing to back the package.

Asked Thursday afternoon if the bill still has a chance, House Appropriations Committee Chairman Hal Rogers, R-Ky., said: "We'll see." He told Fox News that he was at the airport when his secretary told him to return to Capitol Hill.

A joint statement from House Republican leaders said the "situation shows the intense concern within our conference -- and among the American people -- about the need to ensure the security of our borders and the president's refusal to faithfully execute our laws."

In the absence of legislation, Republicans urged President Obama to act on his own to secure the borders and safely deport illegal immigrant children.

"We will continue to work on solutions to the border crisis and other challenges facing our country," they said.

But Senate Democrats blasted their House colleagues for dropping the legislation. "Shame on the House of Representatives," Sen. Chris Murphy, D-Conn., said.

Texas Gov. Rick Perry also slammed his fellow Republicans, saying "it's beyond belief that Congress is abandoning its post while our border crisis continues to create humanitarian suffering."

The legislation's prospects changed quickly over the course of the day. Initially, House leaders thought they had a plan to win enough support, by scheduling a separate vote on legislation to prohibit Obama from expanding a policy that lets some illegal immigrants who came to the U.S. as children stay. Amid reports that the administration is considering such an expansion, the bill by Rep. Marsha Blackburn, R-Tenn., would specifically bar the president from broadening the 2012 policy.

Republicans say another illegal immigrant reprieve by the president would only exacerbate the surge of illegal immigrant children trekking to the U.S.-Mexico border from Central America.

"Such action would create an even greater incentive for more illegal crossings and make the crisis on our border even worse, and that would be a grave mistake," House Speaker John Boehner said Thursday.

The vote had been scheduled by Republican leaders as part of the effort to win conservative support for the separate, scaled-down package giving the Department of Homeland Security an immediate $659 million to address the border crisis and making other policy changes.

But Sen. Ted Cruz, R-Texas, nevertheless raised concerns with House members about their version of the border legislation, and lawmakers and aides said Thursday that it had an impact. They also pointed to opposition from Sen. Jeff Sessions, R-Ala.

Sessions voiced concerns about both the House and Senate proposals, arguing that the Senate would never take up the executive action bill being considered in the House. Sessions wants any bill addressing the president's funding request to also address the executive action issue.

"We as policy makers must face the reality that the president is openly planning to use executive actions to provide amnesty and work permits to millions without any lawful authority," he said in a statement.

Democrats, meanwhile, accused Republicans of playing games.

White House Press Secretary Josh Earnest said earlier in the day: "It is extraordinary that the House of Representatives, after failing for more than a year to reform our broken immigration reform system, would vote to restrict a law enforcement tool that the Department of Homeland Security uses to focus resources on key enforcement priorities like public safety and border security, and provide temporary relief from deportation for people who are low priorities for removal."

Fox News' Chad Pergram contributed to this report.