Lawmakers on Wednesday introduced a new immigration proposal that is poised for a Senate vote this week, one of three narrow proposals that fall short of President Trump's immigration goals, but nonetheless appear to be picking up steam in the Senate.

Republican Sen. Cory Gardner and Democratic Sen. Michael Bennet, both of Colorado, have written a proposal that would provide a pathway to citizenship for so-called Dreamers in exchange for $25 billion for border security and a permanent authorization for employers to voluntarily use the E-Verify system.

Their bill would exclude contentious immigration reform provisions, specifically ending the diversity visa lottery and chain migration, that are stopping the Senate from passing an immigration reform bill.

The Senate is expected to vote on proposals this week as it tries to find a measure that can win the 60 votes needed to pass. Democrats and some Republicans said they believe only a narrow immigration bill can pass the Senate, but even if that turns out to be true, such a bill doesn't seem likely to be acceptable in the House.

"The DACA kids and border security," Minority Leader Chuck Schumer, D-N.Y., said Wednesday, referring to the two elements he and other Democrats support. "That’s the only thing that can pass this chamber. The only thing."

The Gardner-Bennet plan would provide a 12-year pathway to citizenship for Dreamers, who arrived in the U.S. illegally as children.

"This amendment is a reasonable solution to break through Washington gridlock and provide a compromise for Dreamers who are counting on us in Colorado and around the country," Bennet said in a statement.

It would not end chain migration or the visa lottery system, but it does include voluntary E-Verify, which is an electronic method for verifying a person's eligibility to work in the U.S. Mandatory E-Verify has drawn opposition from businesses. That drew a rebuke from the Department of Homeland Security.

“The Gardner-Bennett bill, AKA the Schumer bill, violates the framework, would legalize unlimited numbers through chain migration, and leaves deadly loopholes intact," Katie Waldman, a spokesperson for the Homeland Security Department, told the Washington Examiner.

Still, Democrats are less opposed to it than other GOP immigration reform proposals.

“Coloradans expect Senator Bennet and I to work together, and that's exactly what we have done,” Gardner said. “This legislation addresses DACA and border security, and we are urging members on both sides of the aisle that want a solution to support our bipartisan approach to addressing our flawed immigration system."

Sen. Jeff Flake, R-Ariz., has authored a proposal that would extend the Deferred Action for Childhood Arrivals program, or DACA, in exchange for border security funding.

Sens. John McCain, R-Ariz., and Sen. Chris Coons, D-Del., have proposed similar legislation, but only offers less than $3 billion for border security.

None of the “skinny” bills are backed by the White House.

President Trump said he will only sign a bill that includes the four provision in his plan, which are $25 billion for border security funding, and an end to chain migration and the visa lottery system. In exchange for those reforms, Trump’s plan would provide a pathway to citizenship for Dreamers.