Sen. Tim Kaine Timothy (Tim) Michael KaineBiden promises Democratic senators help in battleground states Second GOP senator to quarantine after exposure to coronavirus The Hill's Morning Report - Sponsored by The Air Line Pilots Association - Pence lauds Harris as 'experienced debater'; Trump, Biden diverge over debate prep MORE (D-Va.) said on Tuesday that he will try to block the Senate from taking a weeklong recess if the government is still partially shut down.

“It would be outrageous for Senators to leave town this Wednesday without fixing this mess, and I object to the Senate going into recess unless Senator McConnell holds a vote on the bipartisan bills the House passed to reopen,” Kaine said in a statement.

The Senate generally leaves town on Thursday, though they’ve been holding brief Friday sessions during the partial shutdown. If the Senate tried to adjourn at the end of the week and Kaine objected, Republicans could force a vote on adjourning.

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House Democrats announced earlier that they were canceling the recess if the government is still shut down.

Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellMcConnell focuses on confirming judicial nominees with COVID-19 talks stalled McConnell accuses Democrats of sowing division by 'downplaying progress' on election security Warren, Schumer introduce plan for next president to cancel ,000 in student debt MORE (R-Ky.) has not yet announced if that chamber will cancel their recess if the government is shut down.

But several Senate Republicans have signaled they believe they should remain in town, even if negotiations are still at a standstill.

“I have encouraged Leader McConnell to cancel next week's recess, so we can continue to work. We need to address this partial shutdown and keep working on the policies and programs important to the American people,” Sen. Joni Ernst Joni Kay ErnstSenators offer disaster tax relief bill Conservatives see glaring omission on Trump's Supreme Court shortlist Senate Republicans scramble to contain fallout from Woodward bombshell MORE (R-Iowa), a member of GOP leadership, said in a tweet.

“I have no idea whether we’re going to have recess or not. My sense is if we’re still in a shutdown we ought not to be going off on recess,” Sen. Lisa Murkowski Lisa Ann MurkowskiGOP ramps up attacks on Democrats over talk of nixing filibuster OVERNIGHT ENERGY: House Democrats tee up vote on climate-focused energy bill next week | EPA reappoints controversial leader to air quality advisory committee | Coronavirus creates delay in Pentagon research for alternative to 'forever chemicals' House Democrats tee up vote on climate-focused energy bill next week MORE (R-Alaska) told reporters on Monday night.