WASHINGTON — With a partial government shutdown grinding into a third week and its disruptive effects widening, Republicans and Democrats agreed on one thing after a weekend of inconclusive staff-level meetings: A breakthrough is probably not imminent.

President Donald Trump on Sunday pressed his demand for billions of dollars in funding to build a southern border wall — something congressional Democrats again declared a non-starter — and once more talked up the prospect of using emergency powers to begin construction. That drew warnings from Democrats that circumventing Congress in that manner would trigger, at the very least, an energetic court challenge.

“We have to build the wall,” Trump told reporters as he left the White House for Camp David, the presidential retreat in Maryland, for staff meetings with border security on the agenda. He said he “may decide a national emergency, depending on what happens over the next few days.”

Neither side reported any real progress in the separate talks held Saturday and Sunday at the White House between Vice President Mike Pence and representatives of House and Senate leaders of both parties. Even as the group was gathering again Sunday, Trump played down the likelihood of a break in the standoff, saying the “very serious talks” would start Monday.

In the meantime, he professed readiness to hold to his demands on the wall, a signature issue of his campaign, before he’ll agree to funding for the quarter of the government that is shuttered as a result of the impasse.

“This shutdown could end tomorrow, and it could also go on for a long time,” the president said.

With Congress set to reconvene Tuesday, Trump — who said prior to the Dec. 22 start of the shutdown that he would be “proud” to trigger one over his wall demands — said the onus was on Democrats to compromise.

But new House Speaker Nancy Pelosi and other Democrats have suggested that the shutdown struggle points to an overarching effort by the president to subordinate lawmakers to his wishes.

“The impression you get from the president: that he would like to not only close government, build a wall, but also abolish Congress so the only voice that mattered was his own,” Pelosi said in an interview aired on CBS’ “Sunday Morning.”

Democrats are seeking to put pressure on Senate Majority Leader Mitch McConnell to get affected government agencies up and running again.

The Kentucky Republican has stayed on the sidelines of the shutdown fight, saying he would only take up appropriations measures that had Trump’s advance approval. McConnell’s stance comes after he led the Senate last month to unanimously approve a government funding bill without the $5.7 billion in wall money the president seeks, only to have Trump reject it despite White House signals that he would go along and negotiate later.

House Democrats plan to pass bills this week that would fund individual government agencies that are affected by the shutdown — at levels the Senate previously approved — but not the wall.

They already approved a measure to fund those agencies collectively on Thursday, but McConnell said the Senate wouldn’t take it up. By putting individual agency appropriations up for a vote, one at a time, Democrats are seeking to force the Republican-controlled Senate to in effect shoulder the blame for preventing the agencies in question from carrying out basic functions.

With the holidays over, the repercussions of the partial shutdown are about to be more widely felt if it persists. The Internal Revenue Service would be unable to issue income tax refunds that taxpayers will expect starting in February, millions of Americans soon will see cuts to food stamps and majestic national parks will continue to be despoiled with trash and human waste. Amid worsening conditions at the most popular parks, the Interior Department on the weekend told park managers to use entrance fees to hire help, according to The Washington Post, though Democrats said such fees are not supposed to go to operations and maintenance.

“What we ought to do is open up the government first, and that’s what we’re going to do,” House Majority Leader Steny Hoyer, a Maryland Democrat, said on NBC’s “Meet the Press.” “I would hope that Senator McConnell would take the responsibility as the leader of the co-equal branch of government, the legislative branch, and send this to the president.”

With financial hardships taking hold among 800,000 federal workers going without pay, Trump said Sunday he understands their situation.

“I can relate, and I’m sure that the people that are on the receiving end will make adjustments. They always do,” Trump said.

And the president insisted, as he has previously, that his demand for wall funding has robust support within the ranks of the unpaid federal workers. “Many of those people agree 100 percent with what I’m doing,” he said.

Trump and his allies contend that backing away from a demand for a solid concrete border wall, in favor of one made of steel, amounts to a compromise, and that the Democrats should respond in kind.

“The barrier or the wall can be of steel instead of concrete, if that works better,” the president said. He said he would ask steel executives for advice on a design.

Democrats, who say a physical barrier is a simplistic and ineffective measure, have proposed $1.3 billion in funding for border security and are pushing for high-tech methods of policing the frontier.

Even as Trump continued to demand funding for the wall as a condition for ending the partial shutdown, his acting chief of staff, Mick Mulvaney, said on CNN’s “State of the Union” that Cabinet secretaries had been told to search for funds “that we can legally use to defend the southern border.”

Mulvaney said Trump’s “authority to defend the nation” would justify the use of emergency powers, including the expenditure of military and other funds, to move ahead with wall-building. But Rep. Adam Smith, the Washington state Democrat who now chairs the House Armed Services Committee, said such a step would leave the White House “wide open to a court challenge.”

Smith added that such a move by Trump “would be a terrible use of Department of Defense dollars.” And Rep. Adam B. Schiff, the California Democrat who became chairman of the House Intelligence Committee last week, dismissed the president’s proposal as an empty threat.

“Look, if Harry Truman couldn’t nationalize the steel industry during wartime, this president doesn’t have the power to declare an emergency and build a multibillion-dollar wall on the border,” Schiff said on “State of the Union.”

Senate Republicans have largely refrained from any criticism of Trump over his hard line, but neither have many publicly cheered him on. And as the deadlock has dragged on, a couple Republican senators facing re-election next year have called for it to end.

One, Sen. Susan Collins of Maine, interviewed on NBC’s “Meet the Press,” ventured a mild dissent.

“It is not a sign of weakness to try to figure out a middle ground,” she said.