By Tal Kopan, CNN

(CNN) -- House Speaker Paul Ryan and other power centers in Congress have begun assembling groups to work on immigration as Washington continues to race the clock ahead of a March deadline to save the Deferred Action for Childhood Arrivals program.

But even with the activity on the Hill, the President continues to wield a heavy influence on any path forward and has shown he can upend any tentative compromise with just a tweet.

Ryan has gathered key Republicans into an informal group to discuss a plan to save DACA, which protects young undocumented immigrants brought to the US as children from deportation, and to discuss what border security and other reform measures Republicans may want.

According to a senior GOP aide speaking on condition of anonymity, the speaker's office has pulled together key members of committees that will play a role in any immigration policy.

The group is a collection of Republicans representing the full spectrum of views within the party, from moderately pro-immigration to heavily favoring tough enforcement and restrictive immigration laws. Veterans of past House efforts to negotiate a bipartisan deal on immigration reform, are also on board.

Politico previously reported on the group.

The group includes Ryan, House Majority Leader Kevin McCarthy, Judiciary Committee Chairman Bob Goodlatte, Judiciary Subcommittee on Immigration and Border Security Chairman Raul Labrador, his predecessor Rep. Jim Sensenbrenner, House Homeland Security Committee Chairman Mike McCaul, Border and Maritime Security Subcommittee Chairwoman Martha McSally, committee member and Texas Rep. Will Hurd, Appropriations Homeland Security Subcommittee Chairman John Carter and Florida Rep. Mario Diaz-Balart.

The aide emphasized that the group is only one of many efforts in the Hill to chart a course, and noted that Ryan and McCarthy also met with their Democratic counterparts and caucus chairs earlier this week.

Nevertheless, if the members involved can reach agreement on a deal, it could bode well for passage. The Republicans included range from those who been pushing for a standalone DACA solution, members who have heavy Hispanic constituencies, to border security hawks, to judiciary committee members who have been pushing some of the most controversial immigration enforcement legislation on the Hill.

Outside of leadership, the conservative House Freedom Caucus has chosen three members to work on the issue, North Carolina Rep. Mark Meadows told reporters earlier this week, and the bipartisan Problem Solvers Caucus is also pulling together a group, Colorado Rep. Mike Coffman said this week.

There's also a separate informal effort by a handful of like-minded Republican moderates who have been meeting since early this year to be ready for a possible immigration reform compromise. First reported by CNN in March, the group is a mix of veterans of past attempts to pull off immigration reform, like Diaz-Balart, and newcomers to Congress.

On the Democratic side, House Minority Leader Nancy Pelosi, Whip Steny Hoyer and the chairs of the Hispanic, Black and Asian-Pacific caucuses met with Ryan and McCarthy this week and Pelosi has had meetings with Trump on the issue.

Her rank and file say they still have confidence in their leadership to represent them in negotiations, but Congressional Hispanic Caucus members have emphasized that they have long worked on immigration reform and should be at the table for any deal.

"I have confidence in our leadership but I think, again, CHC has sort of led on the issue of immigration for several decades now and I think that any agreement over anything that's negotiated has to have CHC buy in," said California Rep. Linda Sanchez, a former CHC chair. "So I think if the president really wants to get this done, CHC should be in the room as well, it's not just leadership."

Still, even with all the groups meeting, all parties know they can be thrown for a loop upon a tweet or word from the President.

Trump met privately with Pelosi and Senate Minority Leader Chuck Schumer on Wednesday night, leaving the Democrats believing they had an agreement to work on a border security package with the bipartisan Dream Act. Trump later tweeted there was no deal, but defended seeking a protection of DACA recipients with "massive border security."

On Friday morning, Trump threw another potential twist in the mix when he tweeted about "chain migration," saying it couldn't be part of any immigration legislation. It remains unclear exactly what Trump meant, but indicates he could push controversial legal immigration overhauls or restrictions or limit protected DACA recipients' abilities to sponsor family members -- all of which could jeopardize any agreement with Democrats.