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 ReidThe Memo: Trump pulls off a stone-cold stunner The Memo: Ending DACA a risky move for Trump Manchin pressed from both sides in reelection fight MORE (D-Nev.) warned last week that any immigration bill must include opportunities for citizenship. 

Sen. Marco RubioMarco Antonio RubioOvernight Defense: Senate passes 0B defense bill | 3,000 US troops heading to Afghanistan | Two more Navy officials fired over ship collisions Senate passes 0B defense bill Trump bets base will stick with him on immigration 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 RyanRyan: Graham-Cassidy 'best, last chance' to repeal ObamaCare Ryan: Americans want to see Trump talking with Dem leaders Overnight Finance: CBO to release limited analysis of ObamaCare repeal bill | DOJ investigates Equifax stock sales | House weighs tougher rules for banks dealing with North Korea MORE (R-Wis.) and the White House offered measured praise, saying the proposal “boded well” for prospects of reaching a deal.