GOP leaders have made clear they don't want this discharge petition effort to succeed.
"Going down a path that results in having a spectacle on the floor that results in a veto doesn't solve the problem," House Speaker Paul Ryan said to reporters last week, who again said he wants to come up with a bipartisan plan on immigration that is acceptable to his party - and not a bill that is backed by Democrats and a few dozen in the GOP.
"We can send the President a serious proposal that addresses immigration, including a permanent solution for those here under DACA, which I believe is an essential aspect of the appropriate path forward on this issue," said Rep. Ryan Costello (R-PA), one of those who signed on to the measure.
The White House has publicly frowned on the efforts by a group of GOP moderates, arguing the effort won't deliver the needed changes sought by the President on immigration.
"We've been clear what our position is," said White House Press Secretary Sarah Huckabee Sanders, as the President has argued for a wide-ranging plan that allows "Dreamers" to get on a 10-12 year path to citizenship, but also includes a number of changes in immigration law, many of which are not acceptable to Democrats.
"We'd still like to see that happen, and we'd love to see a piece of legislation that includes all four of the principles and the pillars that the President outlined," Sanders added.
But the problem for the Trump White House and their Republican supporters is shown in simple numbers - the President only had 39 votes for an immigration plan that he backed in the Senate, and a bill pushed by GOP leaders in the House (which does not have a permanent solution for the "Dreamers") remains far short of a majority as well.
"Certainly we'd love to see something done on immigration," Sanders told reporters on Friday.
"It's been a constant priority for the President," she added.
But while it has been a 'constant priority' for Mr. Trump, he does not have the votes for what he's laid out - either on immigration law changes, or on money for his border wall.
Still, there is no guarantee the discharge petition route will work, and bring the matter to the House floor for a series of votes.
"This is not an easy procedural move to pull off," said ex-Rep. David Jolly (R-FL). "Even more so, it requires breaking with your party's leadership."
This week will show if more GOP lawmakers are ready to take that step.