By ERICA WERNER and DAVID ESPO

WASHINGTON — In a major victory for President Barack Obama, the Republican-led House overcame last-minute opposition from GOP critics on Tuesday and moved toward final passage of legislation to fund the Homeland Security Department without restrictions on immigration.

The bill’s approval was assured after Republicans demanding the bill include constraints on Obama’s immigration policy were turned back on a test vote of 140-278.

Obama’s signature was assured on the measure, which cleared the Senate last week. Without it, short-term funding for the department would expire on Friday at midnight.

Rep. Mike Simpson, R-Idaho, said he, too, opposes Obama’s policy directives that eased the threat of deportation for millions of immigrants living in the country illegally. Yet he also said the “security of the homeland is one of our highest priorities,” and added that Congress could continue to oppose the president without forcing a partial agency shutdown that loomed for Friday.

Not all opponents of the bill were ready to yield.

“If we’re not going to fight now, when are we going to fight?” asked Rep. Matt Salmon, R-Ariz.

The maneuvering on the House floor came after Speaker John Boehner, R-Ohio, told members of his rank-and-file at a closed-door meeting that the time had come to concede defeat after a months-long struggle with the White House and Democrats.

“I am as outraged and frustrated as you at the lawless and unconstitutional actions of this president,” Boehner told the meeting, according to aides. “I believe this decision — considering where we are — is the right one for this team, and the right one for this country.”

He added, “Imagine if, God forbid, another terrorist attack hits the United States.”

A federal judge has blocked implementation of the president’s immigration policies, although the administration has appealed and a final result of the legal challenge is unknown.

Conservatives had demanded that the funding bill roll back Obama’s immigration directives from last fall that spared millions of immigrants from deportation. Democrats had insisted on legislation to fund the department, which shares responsibility for anti-terrorism operations, without any conditions.

The GOP leadership’s decision to bow to Democratic demands angered several conservatives.

“This is the signal of capitulation,” said Rep. Steve King, R-Iowa. “The mood of this thing is such that to bring it back from the abyss is very difficult.”

But more pragmatic Republicans welcomed Boehner’s move.

“Sanity is prevailing. I do give John Boehner credit,” said Rep. Peter King, R-N.Y.

Passage of the stand-alone spending bill would seal the failure of a Republican strategy designed to make Homeland Security funding contingent on concessions from Obama. Controversy over the legislation has produced partisan gridlock in the first several weeks of the new Congress, though Republicans gained control of the Senate last fall and won more seats in the House than at any time in 70 years.

Even so, Democratic unity blocked passage in the Senate of House-passed legislation with the immigration provisions. By late last week, a split in House GOP ranks brought the department to the brink of a partial shutdown. That was averted when Congress approved a one-week funding bill that Obama signed into law only moments before a midnight Friday deadline.

House Republicans said that after months spent railing against Obama’s executive actions, which most Republicans view as an unconstitutional overreach, they had no more moves to make.

House Majority Leader Kevin McCarthy told reporters that with Senate Democrats united to block the House GOP approach, “What direction do we have?”