The White House is holding out hope that immigration reform can still pass this year, bucking the conventional wisdom that the issue is all but dead for now.

“We have an opportunity with a new team in place in the House to act,” said Valerie Jarrett, a senior adviser to President Obama, at a breakfast Friday hosted by The Christian Science Monitor.

On Thursday, House Republicans elected a new majority leader, Rep. Kevin McCarthy of California. He replaces Rep. Eric Cantor of Virginia, who is stepping down next month from his leadership position after his surprise loss on June 10 in the GOP primary. Congressman Cantor’s loss to a tea party-backed candidate was widely seen as dashing any remaining hopes of passing immigration reform, at least this year if not for the rest of Mr. Obama’s presidency.

Ms. Jarrett rejects that idea. Cantor himself has said he did not lose his primary because of immigration reform; polls back him up. But rank-and-file GOP members may still resist acting, given accusations that Cantor favored “amnesty” for unlawful immigrants.

House Speaker John Boehner (R) of Ohio has long maintained he wants to solve the issue, but wanted his members to get through this year’s primaries first. He has also said he wants Obama to show that he can be “trusted” – and that meant not making any more unilateral moves on immigration. Obama has put on hold a review of immigration policy by the Department of Homeland Security.

“He doesn’t want to relieve them [the House] of their responsibility to act right now,” says Jarrett. “And if he were to take action right now, they would use that as an excuse for not acting.”

One year ago, the Senate passed comprehensive immigration reform with strong bipartisan support, but the bill has languished in the Republican-led House. Jarrett says public demand for reform will spur Congress to act.

“What I can tell is that there is a groundswell coming from around the country, and I think that ultimately I am hopeful that that groundswell has an impact on the House of Representatives,” she says. “I think having heard from voices like Rupert Murdoch should be helpful to the Republicans who are nervous.”

Earlier this week, Jarrett discussed immigration reform with the conservative media mogul over dinner at the Blue Duck Tavern here in Washington – an example of her outreach to the business community on the issue.

“Good policy sometimes makes strange bedfellows,” Jarrett says. “I was very heartened by Rupert Murdoch’s passionate interest in immigration reform. He is an immigrant himself. He understands from a business perspective how important immigration reform would be to our economy.”

On Wednesday, the Australian-born Murdoch published an op-ed in The Wall Street Journal, which he owns.

“I don't believe that people come to America to sit on their hands,” Murdoch wrote. “The vast majority of America's immigrants are hardworking, family-minded individuals with strong values.”

Analysts say that Republicans need to move on immigration reform to attract Latino votes, or their prospects in the 2016 presidential election will be limited. The issue is less important in this November’s midterms.

Jarrett repeated the president’s view, that he is open to seeing the House pass individual pieces of legislation, instead of one big bill, “as long as they add up to a whole.”

“What we wouldn’t want to see is just a piece of legislation on border security and high tech immigration without focusing on the path to citizenship for the 11 million people who are here, and other provisions,” says Jarrett. “And so in a sense he leaves it to the House to put [out] a proposal, which we are still waiting to see, for what that piecemeal, if you will, path might be.”