Senate Majority Leader Mitch McConnellAddison (Mitch) Mitchell McConnellBill Kristol resurfaces video of Pence calling Obama executive action on immigration a 'profound mistake' Winners and losers in the border security deal House passes border deal, setting up Trump to declare emergency 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 KaineClinton on GOP promoting Trump 'stronger together' quote: Now copy my policies too GOP promotes Trump line mirroring Hillary Clinton's 2016 campaign slogan Pompeo: US will continue investigating Khashoggi murder 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 TrumpBill Kristol resurfaces video of Pence calling Obama executive action on immigration a 'profound mistake' ACLU says planned national emergency declaration is 'clear abuse of presidential power' O'Rourke says he'd 'absolutely' take down border wall near El Paso if he could 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.