WATCH: Partial government shutdown over DACA unlikely, Rubio says

Sen. Marco RubioMarco Antonio RubioRepublican lawmakers ask Trump not to delay Pentagon cloud-computing contract Overnight Defense: US shoots down Iranian drone | Pentagon sending 500 more troops to Saudi Arabia | Trump mulls Turkey sanctions | Trump seeks review of Pentagon cloud-computing contract EU official in Canada says he feels 'at home' there because no one was shouting 'send him back' 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 KaineOvernight Health Care — Presented by PCMA — Health care moves to center stage of Democratic primary fight | Sanders, Biden trade sharps jabs on Medicare for All | Senate to vote on 9/11 bill next week | Buttigieg pushes for cheaper insulin Health care moves to center stage in Democratic primary fight Dems open to killing filibuster in next Congress 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. 

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"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.