Vice President Joe Biden makes an appearance at a fast held by immigration advocates.

WASHINGTON -- Vice President Joe Biden paid a visit Friday to immigration advocates who have been fasting on the National Mall, lending White House support to the push for House Speaker John A. Boehner to take up the proposed immigration law overhaul now stalled in the House.

“As my father would say, come hell or high water, we’re going to win this,” Biden told the group, according to organizers of the fast, now in its 11th day.

Boehner insisted this week that Republicans in the House are committed to considering immigration legislation, but he declined to say when they would take up the issue. Advocates had urged him to bring the bill to a vote by the end of 2013, but that now seems increasingly unlikely.

The immigration issue deeply divides the GOP, and Republican lawmakers are split over what advocates call the cornerstone of any reform effort -- a route to citizenship for the estimated 11 million immigrants in the country without legal status.

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Advocates are pushing House Republicans to act before Congress recesses for the holidays. Boehner has allowed a bipartisan Senate-passed immigration overhaul to stall, and advocates delivered immigrant-processed turkeys to GOP leaders on the Hill this week and held a vigil outside Boehner’s Capitol Hill townhouse.

The vice president’s visit to the protesters on the Mall follows similar visits from other administration officials and lawmakers.

Labor Secretary Tom Perez visited the group, as did House Minority Leader Nancy Pelosi and two California Republican congressmen, Jeff Denham and David Valadao, who both support an immigration overhaul.

Among those fasting is a top labor leader, Eliseo Medina, the former secretary-treasurer of the Service Employees International Union, who called Biden's visit “inspiring."

“I was humbled and strengthened by his words and commitment to immigration reform,” the 67-year-old longtime immigrant advocate said. “He gives me more hope that we can finally address this moral crisis.”

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lisa.mascaro@latimes.com

Twitter: @LisaMascaroinDC