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.) blocked legislation on Thursday that would have reopened most of the federal government impacted by the partial shutdown.

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.) tried to get consent to take up a House-passed bill that would reopen all agencies except the Department of Homeland Security (DHS), which is at the center of the shutdown fight. But McConnell objected.

The Senate GOP leader didn’t explain his objection from the Senate floor, but he has warned for weeks that he will not bring up a government funding bill unless it’s the product of an agreement between congressional Democratic leadership and President Trump Donald John TrumpHR McMaster says president's policy to withdraw troops from Afghanistan is 'unwise' Cast of 'Parks and Rec' reunite for virtual town hall to address Wisconsin voters Biden says Trump should step down over coronavirus response MORE.

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"The solution to this is a negotiation between the one person in the country who can sign something into law, the president of the United States, and our Democratic colleagues," McConnell said Tuesday when he blocked a House bill as well as a piece of legislation to fund DHS through Feb. 8.

This marks the third time that McConnell has blocked House-passed government funding bills in the past two weeks. Under Senate rules, any senator can ask for consent to vote on or pass a bill, but any senator can object.

Roughly a quarter of the government has been shut down since Dec. 22, forcing roughly 800,000 federal employees to work without pay or be furloughed.

Thursday marks the 27th day of the partial shutdown with no obvious path to a quick end to the funding fight.

Talks between Trump and congressional Democratic leadership derailed after a White House meeting last week. The president left after Speaker Nancy Pelosi Nancy PelosiMcConnell focuses on confirming judicial nominees with COVID-19 talks stalled Overnight Defense: Top admiral says 'no condition' where US should conduct nuclear test 'at this time' | Intelligence chief says Congress will get some in-person election security briefings Pelosi must go — the House is in dire need of new leadership MORE (D-Calif.) said she wouldn't negotiate on the border wall even if the president fully reopened the government.

Tensions further escalated this week with Pelosi asking to postpone the Jan. 29 State of the Union speech and the president, in retaliation, canceling a foreign policy trip she had planned.

Vice President Pence and the president's son-in-law and adviser Jared Kushner Jared Corey KushnerAbraham Accords: New hope for peace in Middle East Tenants in Kushner building file lawsuit alleging dangerous living conditions Trump hosts Israel, UAE, Bahrain for historic signing MORE met with McConnell shortly after the floor drama on Thursday evening, but the GOP leader indicated they had not reached an agreement during their talks.

"We're still obviously discussing the situation and if I have any news to make, I'll let you know," McConnell told reporters.

The Senate passed a stopgap bill late last year by a voice vote, but it was rejected by the White House because it didn’t include extra border money.

Trump is demanding more than $5 billion for his signature wall. Democratic leadership has pointed to $1.3 billion as their cap and argued that it must go to fencing.

Democrats are trying to build pressure on McConnell to move government funding legislation even without Trump's blessing, something members of GOP leadership say is not going to happen.

But Kaine, whose state has a large population of federal workers, will force the Senate to be in session on Friday and Saturday. The Senate will also be in session Tuesday, Wednesday and Thursday of next week, though senators say votes currently aren't scheduled.

Kaine is planning to ask for consent to pass the House package to reopen the government on each of the days, except Saturday. The move will force McConnell or another GOP senator to be on hand to object.

"The first level of illogic we are in is we are punishing the workers and citizens who need services completely unconnected with the border and immigration reform issue," Kaine said on Thursday, about his request to move the package unrelated to DHS funding.

Several GOP senators have backed either taking up the House bills or passing a continuing resolution to reopen most or all of the government while Democratic leadership and Trump continue to fight over border security.

A bipartisan group of senators, led by Sens. Lindsey Graham Lindsey Olin GrahamThe Hill's Campaign Report: Arizona shifts towards Biden | Biden prepares for drive-in town hall | New Biden ad targets Latino voters Senate Democrats' campaign arm announces seven-figure investment to boost Graham challenger Graham: Comey to testify about FBI's Russia probe, Mueller declined invitation MORE (R-S.C.) and Christopher Coons Christopher (Chris) Andrew CoonsBiden promises Democratic senators help in battleground states Shakespeare Theatre Company goes virtual for 'Will on the Hill...or Won't They?' 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-Del.), were drafting a letter to send to Trump to ask him to back a three-week continuing resolution in exchange for the Senate agreeing to take up his border request in the Appropriations Committee as an supplemental appropriations bill.

The idea has received pushback from Republicans and the White House, as well as skepticism from Democrats who are wary of publicly backing the letter without a sense of how much GOP support it has.

But Sen. Susan Collins Susan Margaret CollinsThe Hill's Campaign Report: Biden asks if public can trust vaccine from Trump ahead of Election Day | Oklahoma health officials raised red flags before Trump rally Gideon leads Collins by 12 points in Maine Senate race: poll Senate leaders quash talk of rank-and-file COVID-19 deal MORE (R-Maine), a member of the group, said on Thursday that they had another meeting and were still trying to come up with a proposal along the lines of the one outlined in the letter.

"There are members in good faith who are working on both sides of the aisle, and we continue to have discussions," Collins told reporters. "I've just had a meeting with both some Republican members and some Democratic members to discuss a possible path forward."

Alexander Bolton contributed to this report that was updated at 7:10 p.m.