Donald Trump stood firm on his demand for billions of dollars in funding for a border wall.

The US Senate on Thursday blocked dueling plans to reopen shuttered federal agencies, a fresh setback in efforts to end a month-long government shutdown, but President Donald Trump signaled he could back a "reasonable" proposal that includes border security.

The legislative deadlock left Congress and the president grasping for a solution as thousands of federal workers, some reliant on food banks to make ends meet, are about to miss a second paycheck.

But shortly after the votes, the outlines of a possible deal to end the deepening crisis began to take shape, when Senate leaders huddled in private to discuss a proposal to fund lapsed federal agencies for three weeks, to allow for negotiations over border security.

Asked if he would support the plan, discussed in private by Senate Majority Leader Mitch McConnell and top Senate Democrat Chuck Schumer, Trump was noncommittal, saying he would still want funding for his wall.

"If they come to a reasonable agreement, I would support it," he said, but added: "We have to have a wall in this country."

But top Democrat Nancy Pelosi, the speaker of the House, said any deal that includes a down payment on Trump's wall would be a non-starter.

"I hope that that doesn't mean some big downpayment for the wall," Pelosi said according to US media, adding, "I don't know if he knows what he's talking about."

Trump had backed a Senate measure which would have reopened the government and funded the wall, while a competing Democratic proposal would have opened government through February 8 without funding Trump's wall, and leave room for border security negotiations.

Both bills failed to reach the 60 votes needed to advance in the 100-member chamber.

Trump was already smarting, after being forced into shelving his annual State of the Union address by Pelosi until the government is fully operational.

Though politically bruised, Trump stood firm on his demand for billions of dollars in funding for a border wall as part of an overall budget package.

"We will not Cave!" he tweeted at Pelosi before the Senate voted.

'Nobody knows' what's next

The shutdown was to begin its 35th day Friday, with some 800,000 federal workers left unpaid across the country and in US installations abroad -- and the knock-on effects affecting millions more.

As acrimony in Washington grew, lawmakers across the political spectrum were left scrambling for an exit strategy for the longest-ever halt to federal operations.

"I don't know what's going to happen next. Nobody knows," warned Senate Republican Richard Shelby.

But Lindsey Graham, a Republican senator who often has the president's ear, said he discussed with Trump the new proposal gaining traction: a continuing resolution that funds government for three weeks.

"All of us believe that if we had three weeks with the government open, with all the discord coming from a shutdown, that we could find a way forward to produce a bill that he would sign," Graham said on the Senate floor.

He added in a tweet that Democratic priorities for disaster relief were also included, "showing good faith from both sides."

The White House stressed the need for at least some money for Trump's border plan.

"The three-week CR would only work if there is a large down payment on the wall," press secretary Sarah Sanders said.

Trump has repeatedly called for $5.7 billion in border wall funding, a demand consistently rejected by Democrats.

'Unprecedented'

Senator Mitt Romney, the 2012 Republican presidential nominee, was one of a handful of Republicans who voted for both Senate bills, and he called on congressional leaders and the White House to thrash out their differences quickly.

"We can't just have the lack of communication that prevents us from getting to a deal," Romney told reporters.

McConnell emerged from his US Capitol office to signal the negotiations were ongoing. "At least we're talking," he said.

Meanwhile the shutdown continued to hit American families hard, and employees and agencies have been sounding off about the potential crises ahead.

The air travel industry issued dire warnings, including one from the National Air Traffic Controllers Association.

"In our risk-averse industry, we cannot even calculate the level of risk currently at play, nor predict the point at which the entire system will break," NATCA president Paul Rinaldi said in a statement.

"It is unprecedented."

Earlier Thursday, Trump's billionaire Commerce Secretary Wilbur Ross sparked a backlash by saying "I don't really quite understand why" federal workers were getting food from shelters.

Pelosi pounced.

"This Marie Antoinette attitude of 'Let them eat cake' is pervasive in the administration," she fumed.

"The president thinks, I guess, they can call their dads for money."