House Democrats are renewing their push for a vote on a proposed comprehensive immigration reform package, vowing Tuesday to refocus efforts on pressuring Republicans to sign onto a discharge petition that would force a vote on the legislation.

The immigration reform push is the third recent attempt by Republicans to leverage a discharge petition — a procedural tactic that allows the majority of House members to supersede the will of the House leadership and bring a bill to the floor — in an attempt to force a vote on a piece of legislation that they support.

House Democrats say they currently have 191 signatures — all Democrats — on the petition, and that they will recommit to pressure Republican lawmakers who have said previously that they would support comprehensive immigration reform. The petition must get 218 signatures to force a vote on the legislation.

"We're asking them to put their pen where their mouth is," said Rep. Jared Polis (D-Colo.) in a conference call with reporters Tuesday.

The discharge petition strategy is complicated, and rarely successful. 

The House Democratic caucus includes 199 members — 19 short of the votes needed for a petition to succeed. No House Republicans have said they plan to sign the petition and buck party leaders.

Still, Democratic House members point to the fact that as many as 30 Republicans have said previously that they would vote for an immigration reform bill that includes a pathway to citizenship.

"There are enough votes to get this done," said Rep. Joe Garcia (D-Fla.). "There is a deaf ear. His name is John Boehner."

House Republican leadership has repeatedly said that it would like to take up immigration reform, but some conservatives have declared that a vote on such a bill would doom the GOP in the midterms, throwing cold water on the idea that they would bring up the bill for a vote prior to the election.

"The other way we can bring a bill forward is to go around the speaker," Polis said.

While the prospects of securing a vote on the proposed immigration reform legislation through discharge petition seem unlikely, Democrats note that it is important to show they've exhausted all options to press for the reforms — theoretically affording political cover to President Obama were he to implement reforms via executive order.

Still, Democrats say they'd ideally like to see reforms passed through Congress.

"There is only one way to fix these issues permanently," said Rep. Steven Horsford, (D-Nev.). "And that's with a legislative action."

Democratic aides have also noted that the push for the discharge petition is in large part to mobilize outside groups and build pressure on the House leadership to bring up the bill for a vote. Meanwhile — believing that immigration could become a flashpoint in a handful of competitive races in Arizona, California, Colorado, Texas and Florida, where the issue resonates — Democrats hope that voters will punish Republicans at the ballot box if the GOP refuses to allow a vote.