The highly unusual debate, expected to unfold throughout the week, will test whether a series of legislative concepts and proposals championed by President Donald Trump can garner 60 votes, the threshold for a measure to pass the Senate, the New york Times said.
The Democrats had forced the shutdown in hopes of getting Republicans to approve a permanent solution for beneficiaries of Deferred Action for Childhood Arrivals (DACA).
The push on immigration comes against the backdrop of a ticking clock, and months of congressional inaction.
Launched in 2012 by then-President Barack Obama, DACA has protected some 700,000 young undocumented immigrants from deportation.
In September 2017, Trump announced that he would end DACA on March 5, 2018, and urged Congress to pass legislation to regularise the situation of the beneficiaries, known as "Dreamers".
Trump has put forward an immigration plan that includes a path to citizenship for roughly 1.8 million undocumented young people, while simultaneously demanding $25 billion to build his proposed wall on the Mexican border.
Trump has made it clear that he will not sign legislation that doesn't include money for the wall and limit family migration.
The President's proposal would also place significant new limits to legal immigration, by restricting the issuance of family-reunification visas and eliminating the visa lottery.
With the Senate divided 51-49 between Republicans and Democrats, no bill can gain the necessary 60 votes without bipartisan support.
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