Sen. Chuck Schumer (D-N.Y.) and Rep. Luis Gutiérrez​ (D-Ill.) urged House Republicans to go forward with immigration reform, referencing the primary loss of House Majority Leader Eric Cantor (R-Va.). Some are attributing Cantor's surprise defeat to his position on amnesty. (Theresa Poulson/The Washington Post)

House Majority Leader Eric Cantor’s upset primary loss has scrambled Democrats’ last-ditch strategy aimed at convincing House Republicans to support a legislative overhaul of immigration laws, and also renewed pressure on President Obama to slow the pace of deportations on his own.

The White House and its Capitol Hill allies had hoped to pressure Cantor (R-Va.) to acquiesce to allowing an immigration bill to pass on the House floor by the end of summer. The plan was based on signals that the GOP leadership would be willing to move forward after its caucus was safe from primary challenges on the right.

Cantor’s race was the final obstacle, and Senate Democrats had intended to give floor speeches Wednesday on how the primary season had ended without major tea party victories over incumbents. Obama had also directed his administration to delay a review of immigration enforcement policies until August to avoid a confrontation with GOP leaders and provide them a final window to act before the midterm elections in the fall.

But Cantor’s defeat Tuesday by economics professor Dave Brat — who campaigned heavily against what he called “amnesty” for illegal immigrants — has upended that calculus and emboldened anti-immigration lawmakers. Cantor announced at a news conference Wednesday that he would step down from his leadership post at the end of July, setting off a scramble to replace him.

When asked about immigration, Cantor said he would continue to favor piecemeal reforms rather than one large bill, and he faulted “this my-way-or-the-highway approach that the president has laid out.”

“My position on immigration has not changed,” Cantor said, pointing to his support for legislation aimed at children brought to the United States illegally by their parents. “I have always said the system is broken and needs reforms.”

But Rep. Steve King (R-Iowa) said earlier Wednesday that the Virginia primary result should squelch any chatter of immigration­-related votes ahead of the midterm elections. Republicans hope to make significant gains in the House and Senate by focusing on health care and the economy.

“Moving forward . . . would blow up the caucus,” King said.

Democrats attempted to salvage their strategy Wednesday by minimizing the role that immigration played in Cantor’s loss and pointing to the survival of Sen. Lindsey O. Graham (R-S.C.), who supported a comprehensive immigration bill last year and comfortably won his primary Tuesday.

“You would be hard-pressed to name a constituency more conservative than those who cast ballots in South Carolina,” White House press secretary Josh Earnest told reporters on Air Force One as Obama traveled to Worcester, Mass., for a high school commencement address. Earnest said Graham had made a “persuasive case why comprehensive immigration reform was the right thing for the country.”

Speaking at a Democratic Senatorial Campaign Committee fundraiser in Massachusetts, Obama dismissed the argument that Cantor’s defeat shredded any hope for passing immigration reform. “I fundamentally reject that. I will tell the speaker of the House that he needs to reject that,” the president said.

Dan Pfeiffer, a senior Obama adviser, wrote on Twitter late Tuesday that Cantor’s mistake was in not taking a clear position on the immigration debate. Trying to thread the political needle, Cantor had adopted a position that supported citizenship only for children brought to the country illegally, but he had not scheduled the issue for action on the House floor.

Janet Murguía, president of the National Council of La Raza, said that advocates viewed Cantor as “the singular force blocking reform” and added that he contradicted signals in Washington that he would support legislation by telling voters in his home district that he would block it.

“If the lesson from his loss is to stay away from immigration reform, then that is the wrong lesson,” she said. “That is not going to serve them well in 2016.”

Immigration advocates had split over the White House’s strategy of holding off on potential administration changes until the end of summer.

Those who supported that approach said it was still important to wait to see who is chosen to replace Cantor. The No. 3 House Republican, Majority Whip Kevin McCarthy (Calif.) has been lobbied fiercely by immigrant advocates as a potential supporter of reform.

“This is undoubtedly a setback, but it’s not a fatal blow,” said Kevin Appleby, migration policy director for the U.S. Conference of Catholic Bishops, which supports comprehensive reform.

Groups that opposed the White House delay, on the other hand, said it would be foolhardy for Democrats to continue attempting to persuade Republicans to unite around a Senate immigration plan that has been on the table for a year.

Cantor’s defeat “increases the scope and the urgency on the president to act,” said Chris Newman, legal director at the National Day Laborer Organizing Network. “It makes it more difficult to construct a pathway to victory” in the House.

The debate has been further complicated in recent weeks by a burgeoning crisis in the Rio Grande Valley, where a surge of tens of thousands of unaccompanied children have entered Texas illegally over the past several months.

Republicans have cited the problem as an outgrowth of the administration’s weak immigration enforcement record. GOP lawmakers on Wednesday said Obama’s 2012 decision deferring the deportations of hundreds of thousands of young immigrants had helped create the perception that undocumented youth would be allowed to stay.

Sen. Jeff Flake (R-Ariz.), a member of the bipartisan group of eight senators behind the Senate’s immigration bill, said he saw evidence that the crisis on the border was being driven in part by such perceptions.

Flake and fellow Arizona Sen. John McCain (R) sent Obama a letter asking the president to speak out publicly against the illegal crossings by minors. The administration has said the crisis stems from children fleeing increasing violence in Central American countries.

“We have been pretty clear across the administration about what the law is and how it will be enforced,” Earnest said when asked about the letter.

Al Kamen and Sean Sullivan contributed to this report.