Both Republican and Democratic lawmakers have said they hope to move on the issue, but the parties are split over which measures to approve.

A report last week said Obama intends to push a comprehensive bill that would create a pathway to citizenship for most illegal immigrants. The plan would also institute a national verification system and a guest-worker program. 

Obama spoke of his wish to enact immigration reform in his second inaugural address on Monday. 

“Our journey is not complete until we find a better way to welcome the striving, hopeful immigrants who still see America as a land of opportunity,” said the president, who also touched on the need to boost the number of high-skilled immigrants coming to the U.S.

Many GOP lawmakers have said they would oppose efforts at allowing citizenship, however, calling such measures “amnesty.” Republicans have instead called for strengthening border security. But Senate Majority Leader Harry ReidHarry ReidTop Lobbyists 2017: Grass roots Boehner confronted Reid after criticism from Senate floor GOP in uncharted territory rolling back rules through resolutions MORE (D-Nev.) warned last week that any immigration bill must include opportunities for citizenship. 

Sen. Marco RubioMarco Antonio RubioOvernight Cybersecurity: What we learned from Carter Page's House Intel testimony | House to mark up foreign intel reform law | FBI can't access Texas shooter's phone | Sessions to testify at hearing amid Russia scrutiny Cornyn: Senate GOP tax plan to be released Thursday This week: GOP seeks to advance tax overhaul MORE (R-Fla.), a GOP leader on the issue, unveiled a plan earlier in the month that calls for a path to citizenship, but with illegal immigrants being forced to pay fines and back taxes. 

Rubio has been working to rally conservative support behind his plan, with many Republicans eager to court Hispanic voters, who strongly backed President Obama in the 2012 election.

The plan was backed by Rep. Paul RyanPaul RyanGOP rep: Virginia defeat 'a referendum' on Trump administration After Texas shooting, lawmakers question whether military has systemic reporting problem Pence: Praying 'takes nothing away' from trying to figure out causes behind mass shooting MORE (R-Wis.) and the White House offered measured praise, saying the proposal “boded well” for prospects of reaching a deal.