A network of Latino donors that played a pivotal role in raising money for President Obama’s reelection is now focused on a new campaign: an effort to oust lawmakers who stand in the way of overhauling immigration laws.

The Latino Victory Project, a new political advocacy organization modeled after the Gay & Lesbian Victory Fund, is planning to spend as much as $20 million on campaigns targeting members of Congress who have sizable Latino communities in their districts but oppose comprehensive immigration reform.

At a private meeting for about 30 donors, fundraisers and union leaders Friday, leaders of the group laid out a strategy to make the issue central in next year’s midterm elections if Congress does not pass a bill, identifying 10 House Republicans who would be vulnerable to pressure from Latino constituents.

Members of the group agreed to spend $1 million to $2 million in each of the targeted districts. The effort will begin in coming weeks with a campaign aimed at persuading the lawmakers to back an immigration measure this year. If that fails, the group plans to run a barrage of radio and TV ads against them next year.

“We’re all very united,” said Amalia Perea Mahoney, an art gallery owner in Chicago, who joined donors from Washington, Florida, Texas, California, New York and Massachusetts at Friday’s gathering at a hotel in the District. “I think it’s a pivotal moment.”

Tom Snyder, the AFL-CIO’s immigration campaign manager, said, “There was agreement in the room that if we don’t see action in the House, we know who we’re going after.”

But Rob Stutzman, a GOP campaign consultant in Sacramento, said an intensive media campaign has to be buttressed with a major voter-turnout operation to be effective.

He also said some of the House members on the group’s list may have inoculated themselves by already modifying their stances. One of them, Rep. Jeff Denham (Calif.), announced this weekend that he is backing a Democratic bill that pairs a pathway to citizenship with more stringent border security. “If something doesn’t pass the House, it’s not going to be because of four congressmen from California,” Stutzman said.

The Latino Victory Project grew out of a fundraising committee called the Futuro Fund, which brought in more than $30 million for Obama’s reelection and minted a new cadre of national political donors. Led by actress Eva Longoria, Puerto Rico lawyer Andres Lopez and San Antonio businessman Henry R. Muñoz III, the fund represented the most robust demonstration yet of the Latino community’s ability to amass cash for U.S. political campaigns.

After the election, those involved worked quietly to transform the loose network of donors into a permanent fundraising organization aimed at promoting policy issues and Latino candidates.

“What we want to do with the Latino Victory Project is build political power in the Latino community, so that the faces of Latinos are reflected not just in every level of government but in the policies that drive the country forward,” said Cristobal Alex, a former program officer for the Ford Foundation who left his post to serve as president of the new group.

The project will include a charitable foundation and an issue advocacy arm, on whose board Longoria will serve. The group also plans to engage in elections through a political action committee, which organizers say will be nonpartisan.

Even before it launched, the group’s leaders said they heard from politicians seeking to tap the donor network for support.

“A missing ingredient in the past was Latino financial power,” Alex said. “For the first time, we saw Latinos flex their financial and political muscle.”

It remains to be seen how the group’s immigration campaign will fit into an effort by a coalition of immigrant rights advocates, unions, religious leaders, law enforcement officials and business leaders to drive momentum for a comprehensive bill this year.

Members of that broader coalition have turned out thousands of supporters at events around the country and have financed television ads stressing the economic and law enforcement benefits of revamping the immigration system. Of the estimated $10 million in broadcast TV advertising that has referenced immigration reform this year, supporters have outspent opponents by roughly four to one, according to the ad-tracking firm Kantar Media.

Obama has vowed to continue pushing House Republicans to pass legislation, and he held an event last week at the White House to rally support for a bill.

In a presentation to the Latino Victory Project on Friday, political scientists Gary Segura and Matt Barreto of the polling firm Latino Decisions made the case that opposing an immigration overhaul could permanently harm the image of the GOP in the Latino community. They compared it to the way California Republicans were hobbled after embracing a 1994 state ballot measure aimed at denying education and health benefits to undocumented immigrants.

Latino Decisions identified 10 House Republicans whose reelection bids could be affected by Latino voters in 2014: Reps. Mike Coffman and Scott R. Tipton of Colorado; Denham, Gary G. Miller, David Valadao and Howard P. “Buck” McKeon of California; Daniel Webster of Florida; Joseph J. Heck of Nevada; Stevan Pearce of New Mexico; and Randy Weber of Texas.

The meeting was attended by officials from several labor unions, including the National Education Association and the American Federation of State, County and Municipal Employees, as well as representatives of deep-pocketed backers of liberal causes, including a political adviser to billionaire George Soros.

“There’s a realization that we have to get back to basics,” Snyder said. “. . . We’re at the point where if you don’t act, we’re going to have to make you pay at the ballot box.”