Republican Sen. Bill Cassidy told CNBC on Monday he believes an immigration deal will happen before the next government shutdown deadline in three weeks.

The Senate passed a short-term compromise deal Monday to end the current shutdown, keeping the government funded through Feb. 8. Next, the measure will go to the House and, if approved, to President Donald Trump's desk for a signature.

Immigration had been a sticking point, with Democrats pushing for a deal on the Deferred Action for Childhood Arrivals program, or DACA. The program protects immigrants brought to the U.S. illegally as children.

"Democrats now realize that Republicans are serious about border security. If they want a deal, they are willing to give on border security. And I think frankly Republicans are willing to address the issue of the DACA kids," Cassidy said in an interview with "Closing Bell."

"You put the two together, you can make a deal. So I do think there will be something that happens," he added.

Senate Minority Leader Chuck Schumer, D-N.Y., said Democrats have received assurances that the Senate will take on immigration issues, such as DACA.

Meanwhile, Trump said he was "pleased that Democrats in Congress have come to their senses" in agreeing to end the shutdown, White House press secretary Sarah Huckabee Sanders told reporters on Monday.

Reading a statement from the president, Sanders said Trump was happy that Democrats "are now willing to fund our great military, border patrol, first responders and insurance for vulnerable children."

He said there will be a long-term deal on immigration "if, and only if, it is good for the country."

Cassidy said Trump has four pillars he wants addressed in the deal: DACA, border security, the diversity lottery and family-based sponsorships, also called chain migration.



"If we can address those in a way which is not so expansive that it falls apart but is focused enough on those four issues … then I think a deal can get done," Cassidy said.

— CNBC's Jacob Pramuk and Christina Wilke contributed to this report.