Washington(CNN) After the Senate voted down two proposals to reopen the government on Thursday, lawmakers are searching for a way to end the partial shutdown, though it is still not clear whether Democrats and the White House will be able to find common ground as President Donald Trump continues to push for border wall funding, which Democrats have so far held firm in saying they will not provide.
Shortly after the failed votes -- one on a Republican-backed measure that would have provided $5.7 billion for a border wall and another on a Democratic measure without wall funding -- Senate Majority Leader Mitch McConnell and Senate Minority Leader Chuck Schumer met at McConnell's office in the Capitol.
"We're talking," Schumer told reporters as he left.
White House press secretary Sarah Sanders issued a statement saying that McConnell and Schumer were meeting "to see whether or not they can work out of the deadlock" and indicating that the administration would be open to supporting a three-week stopgap funding measure to reopen the shuttered parts of the government, but only if it included "a large down payment on the wall."
Even amid the flurry of negotiations and support from a bipartisan group of senators to end the impasse over the shutdown, there was to be no deal or breakthrough Thursday night, according to two sources familiar with the talks.
McConnell, asked about what kind of progress had been made as he departed the Capitol, said only: "Well, at least we're still talking."
The issue remains an inability to pin down exactly what the President would accept in any type of deal, the sources said, and there is still no clarity on the next steps. Talks are expected to continue, but at the moment the dynamics that led to the now 34-day-old shutdown don't appear to have shifted in a meaningful way, one of the sources said.
Schumer spokesman Justin Goodman said, "Sen. Schumer and Senate Democrats have made clear to Leader McConnell and Republicans that they will not support funding for the wall, prorated or otherwise."
House Speaker Nancy Pelosi had said as she was leaving the House floor that she hopes any potential agreement between McConnell and Schumer will not include a down payment on the wall.
"The President just said that if they come to a reasonable agreement he will support it," she said. "I hope it doesn't mean some big down payment for the wall."
Asked again about a potential down payment, she said: "That is not a reasonable agreement between the senators."
Trump had suggested to reporters on Thursday that one of the ideas being floated by Congress is a "prorated down payment" for a border wall.
"One of the ideas suggested is they open it, they pay some sort of prorated down payment for the wall, which, I think people would agree, you need," he said.
Republican Sen. Lindsey Graham of South Carolina, a close ally of the President, offered his support for the idea of a "down payment."
In a statement, Graham said, "The way forward is clear to me: a three-week continuing resolution that includes a down payment on wall/barrier funding and priorities of Democrats for disaster relief, showing good faith from both sides."
But in addition to Pelosi's pushback, some Senate Democrats were quick to throw cold water on the idea of a down payment for the wall in exchange for a short-term funding bill.
Sen. Debbie Stabenow of Michigan, a member of Senate Democratic leadership, said giving in to Trump would mean that the White House would use a shutdown to get whatever it wanted next time.
"What does he hold workers' wages hostage for next? How many times will he try to hold wages hostage?" the senator asked.
Sen. Angus King, a Maine independent who caucuses with Senate Democrats, said: "He is basically saying, 'Give me what I want -- or give me part of what I want -- or I'll shut the government down.' ... I don't like rewarding shutdown politics."
A senior Democratic aide told CNN that lawmakers are indeed talking and attempting to work something out, but rejected the idea of a down payment on a border wall, large or otherwise, citing the fact that the President's proposal to reopen the government with wall funding included had received fewer votes than the Democratic proposal on the floor.
"Look what just happened on the floor -- the idea he has leverage here is not in touch with reality," the aide said.
And even as lawmakers discuss the possibility of a short-term measure to fund the government, Trump again raised the prospect of finding other ways to pay for a border wall without congressional approval.
"I have other alternatives if I have to and I'll use those alternatives if I have to," the President said on Thursday.
This story has been updated with additional developments.