Senate Majority Leader Mitch McConnellAddison (Mitch) Mitchell McConnellGOP Green New Deal stunt is a great deal for Democrats The national emergency will haunt Republicans come election season Trump: McConnell should keep Senate in session until nominees are approved 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 KaineOvernight Defense: Trump declares border emergency | .6B in military construction funds to be used for wall | Trump believes Obama would have started war with North Korea | Pentagon delivers aid for Venezuelan migrants Kaine asks Shanahan if military families would be hurt by moving .6B for border wall Clinton on GOP promoting Trump 'stronger together' quote: Now copy my policies too 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 TrumpMcCabe says he was fired because he 'opened a case against' Trump McCabe: Trump said 'I don't care, I believe Putin' when confronted with US intel on North Korea McCabe: Trump talked to me about his election victory during 'bizarre' job interview 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.