Sens. John McCain and Chris Coons on Monday are unveiling a bipartisan immigration measure that would protect so-called "Dreamers" from being deported, provide a path to citizenship and provide new border security measures without funding for a wall.

The legislation is a companion to a bill introduced in the House by Reps. Will Hurd, R-Texas and Pete Aguilar, D-California, which has 54 co-sponsors -- 27 Republicans and 27 Democrats. The McCain-Coons bill would "allow Congress to focus on other pressing matters, including a budget deal to fully fund the military," their offices said.

"While reaching a deal cannot come soon enough for America's service members, the current political reality demands bipartisan cooperation to address the impending expiration of the DACA program and secure the southern border," said McCain, who has been working from Arizona since late last year as he deals with treatment for brain cancer.

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McCain added that their bill would "address the most urgent priorities of protecting Dreamers, strengthening border security, alleviating the backlog in immigration courts, and addressing the root causes of illegal immigration."

Coons told CBS News' Nancy Cordes that McCain is "determined to break the impasse on funding for the armed forces by solving the DACA/border issue" and "Hopefully it will restart the discussion on how to move ahead on a total deal by Thursday." Coons said that he's still hopeful that the bipartisan, Collins-Manchin "common sense coalition" will produce a broader deal on immigration this week. If they don't, he said, the McCain-Coons bill could serve as the base bill for a broader deal that includes defense and nondefense domestic spending.

Congress faces a Thursday deadline to pass a new government funding bill or risk another government shutdown. The government shut down for three days last month after Democrats blocked a short-term spending bill offered by Republicans because there was not yet an agreement on immigration. The Trump administration ended the 2012 Deferred Action for Childhood Arrivals (DACA) program created by President Obama last fall, and has tasked Congress with finding a legislative solution to it by March 5.

The challenge remains that House conservatives are opposed to Hurd-Aguilar-McCain-Coons. They want to see more immigration reforms in exchange for DACA protections.

CBS News' Nancy Cordes contributed to this report.