WASHINGTON — In a last-ditch effort to bring an immigration overhaul to a vote in Congress, House Democrats on Tuesday began targeting key GOP lawmakers in hopes of pressuring House Speaker John A. Boehner to act.

The election-year campaign against 30 House Republicans, who have expressed interest in changing the nation’s immigration laws, was framed by Democrats as one last opportunity to engage in a legislative debate before President Obama begins taking executive actions.

The administration has indicated it plans to halt strict enforcement of some immigration laws, including deportations that separate families, if Congress fails to act. Obama met Tuesday with faith leaders as protesters continued their second week of vigil in front of the White House.

“The president’s going to be forced to act,” said Rep. Joe Garcia (D-Fla.), a chief sponsor of a bipartisan bill that has sat idle in the House.

Boehner has tried to nudge the Republican majority to consider immigration reform, but lawmakers have been cool to the issue. Only three have signed onto the House bill.

A sweeping package approved last year in a robust bipartisan vote in the Senate landed with a thud in the House, where many Republicans from congressional districts with few minority residents have little interest in the issue. But GOP elders believe immigration reform is paramount to expanding the party’s voter base before the 2016 presidential election.

The inaction has left immigration advocates increasingly frustrated with Obama, but the administration has urged them to focus instead on Republicans as the main obstacle to reform.

The effort launched Tuesday is a long-shot attempt to force a floor vote through procedural methods. Under House rules, Boehner would be forced to allow the vote if a majority of lawmakers sign a so-called discharge petition. Democrats are about two dozen signatures short of the 218 needed, and are targeting those key Republicans to make gains.

Both sides acknowledge that if the vote was held, the legislation may, in fact, pass, which could prove thorny for Republicans from conservative districts where many voters criticize the reform bill as “amnesty” for immigrants.

The measure would beef up border security and guest worker programs, while allowing a route to legal status for those who have immigrated illegally. It is similar to the bill that was approved by the Senate.

The White House is expected to announce some changes in immigration law in the weeks ahead, and more if Congress fails to act this summer.

lisa.mascaro@latimes.com

Twitter: @lisamascaroinDC