Washington (CNN) Donald Trump is threatening to burst out of his dead end on the government shutdown by wielding sweeping presidential power to declare a national emergency to bypass Congress and build his border wall.

Trump's gambit comes as House Speaker Nancy Pelosi gears up to pile political pressure on the GOP this week with a set of bills designed to open shuttered agencies and show that Democrats can provide credible government.

But since the Republican-led Senate will only act on a deal that Trump will sign, the parties remain as estranged as ever as the shutdown heads into a third week with hundreds of thousands of government workers unpaid.

"We're looking at a national emergency because we have a national emergency -- just read the papers," Trump told reporters at the White House on Sunday.

Trump's threat is a characteristic move from a President who often tries to escape a crisis by igniting an even bigger controversy, hoping to throw his enemies off balance and disguise his own vulnerable position.

But such a declaration could ignite a legal and political firestorm if he goes ahead, escalating the bitter showdown over the wall and his hardline immigration policies into a constitutional duel over executive power.

Talks over the weekend involving congressional staffers and led by Vice President Mike Pence failed to make meaningful progress toward ending the standoff. Trump is demanding more than $5 billion in wall funding before agreeing to reopen the government. Democrats have offered about $1.5 billion for border security, but no taxpayer dollars for a wall, which the President promised Mexico would pay for.

Both sides appear to be digging deeper into a showdown that is exacerbated because it is the first test of wills in the new era of divided government after Democrats took control of the House of Representatives last week.

"This shutdown could end tomorrow, and it could also go on for a long time. ... It's really dependent on the Democrats," Trump said on Sunday.

But the Democrats are refusing to talk about Trump's wall while the government remains partially closed.

"There's no requirement that this government be shut down while we deliberate the future of any barrier, whether it's a fence or a wall," said Democratic Senate Minority Whip Dick Durbin on "Face the Nation" on CBS.

"This is the first President in history who shut down his own government," he said.

The extent of disagreement was reflected in differing accounts of the fruitless attempts to negotiate a deal coming from each side.

A source in Sunday's meeting involving Pence, White House staffers and congressional aides told CNN's Manu Raju there was no real discussion about a dollar amount that could help unpick the deadlock.

And a Democratic source familiar with the talks said the administration could not provide a full accounting of how Trump would spend his billions of dollars as requested.

A House GOP leadership aide said, "Democrats were given what they asked for, which was a detailed, breakdown list of the administration's proposals for border security that include the wall and other border protection measures."

How shutdowns end

Government shutdowns usually end when one or both sides in the dispute start to feel intolerable political pain and take steps to end it.

So far, that point has not been reached in the current standoff.

The President, who has made few attempts to broaden his support in office appears to most fear a backlash from conservative media and his own base that is passionately in favor of his promise to build a wall.

He may be less vulnerable to anger in the political middle ground of America than most presidents as the devastating effects of no paychecks, closed national parks and curtailed government services start to build.

Trump also does not seem that troubled by the plight of locked out government workers -- who he once said were mostly Democrats anyway.

In a news conference on Friday, the President suggested, without evidence, that many government workers want the government to stay closed until he gets wall money.

Democrats are also yet to feel a compelling reason to end the shutdown. Few want their new House majority to begin by handing Trump a win, and since Trump said before Christmas he would be proud to shut down the government, they believe that he will get most of the blame.

But the longer the shutdown goes on, there must be some danger that Democrats come to be seen as just another example of Washington dysfunction -- in a way that taints their hopes of a fast start in the House.

Does Trump have the power to go it alone?

Given Trump's volubility, it is not always easy to judge whether his threats -- like declaring a national emergency to fund the wall -- are negotiating tactics, serious gambits or just ideas that occur in the spur of the moment.

But a bold claim of presidential power would be in line with his tendency to test the limits of his executive authority and his impatience with constitutional constraints.

Opinion in Washington is divided on whether Trump actually has the power to barge ahead on his own on the wall -- despite opposition in Congress.

House Intelligence Committee Chairman Adam Schiff said on CNN's "State of the Union" on Sunday that Trump could not "execute" on his "threatening talk."

"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. So, that's a nonstarter," Schiff said.

But Rep. Adam Smith, the chairman of the House Armed Services Committee, was asked whether Trump had such authority on "This Week" on ABC.

"Unfortunately, the short answer is yes," he said in the belief that Trump could declare an emergency in order to use Defense Department dollars in a building project as had been done in Afghanistan and Iraq.

But Smith also warned: "I think the President would be wide open to a court challenge saying 'Where is the emergency?' "

White House press secretary Sarah Sanders came unstuck on this score when she was challenged on "Fox News Sunday" over the White House claim that 4,000 known or suspected terrorists had come into the United States and that the most vulnerable access point was the southern border.

In fact, according to the Department of Homeland Security, the figure represents individuals blocked from traveling or entering the United States, often at airports and does not necessarily refer to the southern border.

If Trump does make good on his threat to declare a national emergency, he would be on contested ground.

He would arguably be seeking to use unchecked executive power to subvert a coequal branch of government that has thwarted him in carrying out a personal political crusade.

And he would again be accused of using the military to further his own ends, as he was when he sent troops to the border region last year.

US law does give a President the authority at times of national emergency to defer Army construction plans that are not essential to national defense and to apply the resources to civil works projects that meet that test.

But such power is generally seen to be limited to a time of war or genuine national crisis. Trump's declaration would likely face a legal challenge on the grounds that the situation at the border does not meet that sudden contingency. The judiciary and Congress also have the right to challenge a President's definition of a national emergency.

Such a power play would also come at a time when there are already worries about the President's impulsive leadership.

Constraints on Trump are weakened by the departure of moderating influences in his administration, like former Defense Secretary James Mattis.

He is currently being served by an acting defense secretary, an acting attorney general, an acting White House chief of staff and a White House counsel's office that is regarded as understaffed.

Such aides may lack the authority or the desire to question the legality or wisdom of the President's actions.