WASHINGTON (NewsNation Now) — The Democratic-controlled House of Representatives is poised to vote this week on two immigration bills: one that would forge a pathway to citizenship for “Dreamers” and another that would make it easier for many immigrant farmworkers to stay in the U.S.

The bills are an effort to take targeted steps forward while lawmakers discuss President Joe Biden’s comprehensive immigration plan, and initial procedural steps could come as early as Tuesday. 

The first immigration bill expected in the House this week would offer an eventual path to citizenship to “Dreamers,” U.S. residents brought to the country illegally as children. It would also help recipients of temporary migration protections that allow immigrants from several disaster- or conflict-hit countries to live temporarily in the country.

The measure, sponsored by Democratic Rep. Lucille Roybal-Allard of California, could help make over 4.4 million people eligible for permanent U.S. residence, according to the Migration Policy Institute. It passed the House once already, in 2019, with 237 votes. Seven of those votes were Republicans.

The second bill, sponsored by Democratic Rep. Zoe Lofgren of California, would put about a million undocumented farmworkers on a path to citizenship, a Democratic aide said. It has a Republican co-sponsor, Rep. Dan Newhouse of Washington state. Thirty-four Republicans voted for the measure when it last passed the House in 2019.

Neither bill was taken up in the Senate when it had a Republican majority. With Democrats now holding narrow control of that chamber, they hope to be able to attract some Republican support.

But Sen. Lindsey Graham, one of the leading Republicans in past talks on immigration, said he was doubtful bipartisan progress could be made on legislation before the latest spike in border arrivals has been halted.

U.S. authorities saw a 60% increase in children crossing the southwest border alone between January and February to more than 9,400.

Nearly 4,300 unaccompanied children were being held by border patrol officials as of Sunday, according to an agency official who requested anonymity to discuss the matter. 

“I think it’s gonna be really hard to get a bipartisan bill put together on anything that has a legalization component until you stop the flow,” Graham told reporters on Monday evening.

Democrats last month formally introduced Biden’s sweeping immigration overhaul in Congress, a measure that would provide a path to U.S. citizenship for an estimated 11 million immigrants in the country illegally. It faces long odds to passage as no Republicans have supported it publicly and it’s unclear whether all Democrats back the approach.

Sen. Dick Durbin, a leader of Senate Democrats’ drive to help millions of immigrants become citizens, cast doubt on its prospects on Monday.

Durbin said Graham’s insistence on addressing the stream of migrants at the border would make it hard to deal even with individual, broadly popular immigration proposals. 

“When we start getting into the other areas, it gets much more complicated. He knows that,” Durbin said of Graham. The Democrat added later, “I wish we could move one piece at a time, but I don’t think that’s in the cards.”

But Durbin said that once the House has passed the two immigration measures this week, he and other senators will have to look for bipartisan consensus on a bill “with those two as the starting points.” 

Reuters and the Associated Press contributed to this report. All reporting by Reuters’ Susan Cornwell and AP’s Alan Fram.