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WATCH: Partial government shutdown over DACA unlikely, Rubio says

Sen. Marco RubioMarco Antonio RubioTrump must send Russia powerful message through tougher actions McCain, Coons immigration bill sparks Trump backlash Taking a strong stance to protect election integrity MORE (R-Fla.) predicts lawmakers will not shut down the government if they fail to reach a deal on a variety of immigration issues. 

“These things come together quickly usually at the last possible moment,” Rubio told The Hill. “I don't believe there will be a government shutdown.” 

Sen. Tim KaineTimothy (Tim) Michael KaineKaine hits Trump over shutdown threat: If you don't want to work, take some extra 'executive time' Dem senators tell Trump he doesn’t have ‘legal authority’ to launch preemptive strike on North Korea McConnell must go nuclear: Abolish the legislative filibuster MORE (D-Va.) thinks that negotiators are likely to reach agreement on a fix for immigration-related matters that bipartisan lawmakers insist happen before agreeing to fund the government before the end of next week. 

"We ought to be able to find a deal," Kaine said, before Jan. 19, the deadline to pass a government funding bill.

A small group of bipartisan senators said they reached a deal Thursday on efforts to protect about 800,000 people covered by the Deferred Action for Childhood Arrivals (DACA) program who face possible deportation over President Trump’s winding down of the Obama-era program. Their talks also cover the diversity visa system, family-based migration and border security.

Kaine predicted there will be Democratic votes for a package that includes security and DACA language.

“I was willing to vote for both. So, if we can find a deal, and there’s no reason we shouldn’t since so many of us in the Senate voted for both permanent protection for Dreamers and border security, we ought to be able to find a deal before the 19th,” Kaine said. 

Watch the video above to hear the senators in their own words.

- This report was updated on Jan. 12 at 1:06 p.m. to clarify Sen. Kaine's comments.