Senate Majority Leader Mitch McConnellAddison (Mitch) Mitchell McConnellThe Hill's Morning Report - Presented by Facebook - Americans debate life under COVID-19 risks The 10 Senate seats most likely to flip Democratic leaders say Trump testing strategy is 'to deny the truth' about lack of supplies MORE (R-Ky.) blocked legislation on Wednesday that would reopen most of the government currently closed during the partial shutdown.

Sen. Tim KaineTimothy (Tim) Michael KaineBipartisan senators introduce bill to make changes to the Paycheck Protection Program Overnight Defense: National Guard chief negative in third coronavirus test | Pentagon IG probing Navy's coronavirus response | Democrats blast use of Russia deterrence funds on border wall Overnight Defense: Navy secretary nominee: Service in 'rough waters' after 'failure of leadership'| Senate fails to override Trump's Iran war powers veto| Top Armed Services Republican expects to address Pentagon border wall funds in defense policy bill MORE (D-Va.) went to the Senate floor to ask for consent to take up the House-passed bill that would fund every agency and department impacted by the partial shutdown, except the Department of Homeland Security, through Sept. 30.

McConnell, however, objected. It's the fourth time he's blocked the bill to reopen most of government. He has also blocked, as recently as Tuesday, a House-passed bill to fund the Department of Homeland Security through Feb. 8.

Democrats have been coming to the floor on a near-daily basis while the Senate is in session to try to bring up the House package, even though the GOP leader has said he will not allow them to come to the Senate floor.

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Under Senate rules any one senator can try to pass a bill, but any one senator can also object.

The partial government shutdown, which is currently in its 33rd day, is impacting roughly a quarter of the government and forcing approximately 800,000 employees to work without pay or be furloughed.

The back-and-forth on the floor comes a day before the Senate is expected to hold votes on dueling proposals that would fully reopen the government.  

The first proposal, which is backed by the White House, includes $5.7 billion for the wall in exchange for a three-year extension of protections for Deferred Action for Childhood Arrivals program recipients and some Temporary Protected Status holders. 

McConnell is publicly pushing Democrats to support that proposal, even though it's expected to fall short of the 60 votes needed to break a filibuster. 

"The president went out of his way to include additional items that have been priority areas for Democrats," McConnell said on Wednesday. 

If that White House-backed measure does not get 60 votes, the Senate will then take a second vote on a proposal to temporarily reopen the government with a continuing resolution (CR) through Feb. 8. 

Democrats say that President TrumpDonald John TrumpMulvaney: 'We've overreacted a little bit' to coronavirus Former CBS News president: Most major cable news outlets 'unrelentingly liberal' in 'fear and loathing' of Trump An old man like me should be made more vulnerable to death by COVID-19 MORE has to reopen the government before they will negotiate. They worry that making a deal while the government is closed would set the precedent for shutting down the government as a negotiating tactic. 

But that bill is also unlikely to get 60 votes. The Senate passed a CR to fund a quarter of the government through Feb. 8 by voice vote late last year, but Trump then came out against the measure.