"Yes, it's going to happen right here - stay tuned," Illinois Democratic Senator Dick Durbin said in a recent floor speech. "Next week could be historic."
President Donald Trump has consistently framed immigration reform as a security matter, first and foremost.
"Glaring loopholes in our laws have allowed criminals and gang members to break into our country," Trump said in his weekly address, issued Sunday. "During my State of the Union, I called on Congress to immediately close dangerous loopholes in federal law that have endangered our communities and imposed enormous burdens on U.S. taxpayers."
Of immediate concern to many lawmakers of both political parties are hundreds of thousands of young undocumented immigrants soon to be at risk of deportation. Some Republicans also want to reshape and restrict legal immigration, which could have a major impact on those aspiring to come to America from around the world.
Trump set the stage for the upcoming debate last year, when he terminated Deferred Action for Childhood Arrivals, or DACA, a program that granted temporary work and study permits to immigrants brought illegally to America as children, and gave Congress a March 5 deadline to address their plight.
"At that point [March 5], 1,000 young people each day, on average, will lose their protection from deportation and their legal right to work in America," Durbin said.
FILE - U.S. President Donald Trump listens to U.S. Senator Dick Durbin, D-Ill., during a meeting with legislators on immigration reform at the White House in Washington, Jan. 9, 2018.
"I see this as an opportunity for these individuals who have literally grown up in our country to be able to be full participants in our country," Republican Senator James Lankford of Oklahoma said.
The president has made clear he wants more than a DACA fix.
Secretary of Homeland Security Kirstjen Nielsen and President Donald Trump listen to Rep. Peter King, R-N.Y., during a meeting with law enforcement officials on the MS-13 street gang and border security, in the Cabinet Room of the White House, Feb. 6, 2018.
"We need the [border] wall. We're going to get the wall," Trump said at the White House last week. "We've identified three priorities for creating a safe, modern and lawful immigration system: securing the border, ending chain migration, and canceling the terrible visa lottery."
Aside from building a wall along the U.S.-Mexico border, Trump has proposed lower the number of immigrants America accepts from around the world and prioritizing newcomers with advanced work skills.
Democrats say they are open to a smaller deal, legal status for DACA recipients, also known as Dreamers and beefing up U.S. borders.
"There's an appetite on both sides and in both chambers to get this done, both helping the Dreamers and border security," Senate Minority Leader Chuck Schumer of New York said.
Senior Republican lawmakers say Trump deserves credit for the totality of his immigration proposal.
"President Trump has done something that President Obama never did. He's offered 1.8 million young adults who are currently DACA recipients and DACA-eligible an opportunity to get on a pathway to American citizenship," Republican Senator John Cornyn said. "That's an incredibly generous offer."
Senate Majority Leader Mitch McConnell, a Kentucky Republican, has not speculated what, if anything, the chamber might pass.
"While I obviously cannot guarantee any outcome, let alone supermajority support, I can ensure the process is fair to all sides, and that is what I intend to do," McConnell said last week.
"We're not going to solve the whole problem in this next week," Maine independent Senator Angus King warned. "We are not going to solve all of the complicated - and believe me they are complicated - issues."
McConnell promised an open debate, meaning there is no time limit and senators of both parties can, in theory, offer an unlimited number of proposals for the chamber to consider. Anything the Senate approves would need to pass in the House of Representatives and get Trump's signature to become law.