Undaunted by GOP efforts to undo President Obama's executive order to halt deportations, House Democrats have launched a national campaign to get the millions of eligible illegal immigrants signed up.

Spearheaded by Rep. Luis Gutiérrez (D-Ill.), the multi-city effort will unite lawmakers, faith-based institutions and other community leaders working to help participants through the application process and over other bureaucratic hurdles.

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"We want to ensure that … constituents understand what the executive order does, that those eligible will be able to come forward safely to submit to a background check and to register in order to get right with the law," Rep. David Cicilline (D-R.I.), who will host such an event on Wednesday in Providence, said Tuesday during a press briefing in the Capitol.

Rep. Jared Polis (D-Colo.) said the involvement of lawmakers is "absolutely critical" to the success of the program, especially amid conservative attacks that advocates fear could depress participation.

"We need to convey the message that it is here to stay," Polis said of the program.

The campaign is evidence that the Democrats are confident the Republican efforts to undermine Obama's executive actions will fail this year.

House Republicans this week are pushing a series of amendments that would not only block Obama's move to halt deportations for as many as five million illegal immigrants, but also eliminate the president's 2012 deferred action program, which allows high-achieving illegal immigrants brought to the country as youngsters to stay and work.

The Republicans intend Wednesday to attach those provisions to legislation funding the Department of Homeland Security (DHS) beyond February. Amid the heightened terrorist threats highlighted by recent attacks in Paris, GOP leaders are hoping both Senate lawmakers and Obama will be forced to accept at least some of those amendments for the sake of keeping the DHS up-and-running.

Democrats, however, have other ideas. The White House on Tuesday issued a veto threat against the DHS package if the immigration amendments are attached, and Democratic leaders are confident they have the congressional support in both chambers to uphold it.

"The president has been absolutely clear. We're absolutely clear. The executive order stands, it's constitutional … so there's really no reason to negotiate," Gutiérrez said.

"There is no divide in the Democratic Caucus on this issue," he added. "If any of these poison pills are attached, I expect the president of the United States to carry out his veto threat, and I expect the Democrats to sustain that veto threat. … There's an important number, and it's two-thirds, and they don't got it."

Democratic leaders are accusing the Republicans of playing politics with the DHS bill at the threat of national security. Rep. Bennie Thompson (Miss.), senior Democrat on the House Homeland Security Committee, said Tuesday that the GOP amendments are designed only "to placate the extreme right wing of the Republican Party."

Rep. David Price (D-N.C.), ranking member of the Appropriations Committee's subpanel on homeland security, called the tactic "an outrageous abuse of the appropriations process" that "puts our country in jeopardy."

And House Minority Leader Nancy Pelosi (D-Calif.) echoed that message.

"They know this won't become the law," Pelosi said. "They're hoping the Senate will bail them out."