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WATCH: Partial government shutdown over DACA unlikely, Rubio says

Sen. Marco RubioMarco Antonio RubioThe Memo: Saudi storm darkens for Trump GOP leaders hesitant to challenge Trump on Saudi Arabia On The Money: Treasury official charged with leaking info on ex-Trump advisers | Trump to seek 5 percent budget cut from Cabinet members | Mnuchin to decide by Thursday on attending Saudi conference 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 Defense: Trump says 'rogue killers' could be behind missing journalist | Sends Pompeo to meet Saudi king | Saudis may claim Khashoggi killed by accident | Ex-VA chief talks White House 'chaos' | Most F-35s cleared for flight Democrats torch Trump for floating 'rogue killers' to blame for missing journalist Election Countdown: O'Rourke brings in massive M haul | Deal on judges lets senators return to the trail | Hurricane puts Florida candidates in the spotlight | Adelson spending big to save GOP in midterms 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.