WASHINGTON – The partial government shutdown over funding for a border wall reached a milestone Sunday, now tying for the third longest on record without any end in sight because of bitter negotiations.

As President Donald Trump insisted that the border wall dispute was a "very important battle," his aides indicated that he wouldn't cave on his demands.

White House press secretary Sarah Sanders said Sunday that Trump "absolutely" stands by his comments that he is willing to continue the shutdown for months, or even years, to get the money he wants to build a wall along the U.S.-Mexico border. Sanders said the wall is needed to address the "national crisis" at the southern border.

Democrats insist a wall is an ineffective use of resources. They are pushing for a more varied approach to border security, which includes improved technology to monitor the border with tools such as drones and tunnel detection.

White House Chief of Staff Mick Mulvaney – who in 2015 said a border barrier as "the end of an immigration discussion" was an "absurd and almost childish" solution to U.S. immigration issues – said Sunday that the wall would only be one component of the $5.6 billion Trump wants for border security.

"We recognize that things like technology are important," Mulvaney said on CNN's "State of the Union." "But certainly a barrier is important."

The definition of that barrier has evolved over time. On the campaign trail in 2016, Trump insisted it would be a "big, beautiful" wall made of concrete – and that Mexico would pay for it. Mulvaney said Sunday on "Meet the Press" that the president is now willing to compromise by backing off the demand for a concrete wall to "replace it with a steel fence."

"If that is not evidence of the president's desire to try to resolve this, I don't know what is," Mulvaney said.

Democrats say they are willing to discuss what is needed to address to border security and immigration, but only after the shutdown ends.

"What we ought to do is open up the government first," said House Majority Leader Steny Hoyer, D-Md., Sunday on "Meet the Press."

"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 Sen. Dick Durbin, D-Ill., on CBS' "Face the Nation."

Senior congressional aides and top White House officials, including Vice President Mike Pence, met again Sunday in the nation's capital after hours of talks the previous day did not lead to a compromise. But no deal was made, and no further meetings for the group are scheduled, according to a Democratic official familiar with the meeting.

On Saturday, Democrats asked the White House for a budget justification for the requested funds, which were not included in the administration’s 2019 budget. That justification was not completed Sunday, the official said.

Pence's office described Saturday's meeting at the Eisenhower Executive Office Building, next door to the White House, as "productive" with Democratic sources saying those in the room urged Trump to reopen the government and back off his request for more than $5 billion to construct a wall along the southern U.S. border.

Mulvaney said he thought the meeting was "disappointing" and that Democrats were not looking for a solution "because they think that they are winning this battle politically."

The president admitted on Twitter after the Saturday meeting that "not much headway" was made during the talks but again pressed for border security, a sign neither side is wavering in the bickering that has left thousands of federal employees working with no pay.

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The president spent much of the day Saturday attacking Democrats, the media and making a case for the wall by saying everyone besides "drug dealers, human traffickers and criminals" wants one.

The House and the Senate adjourned Friday and members aren’t scheduled to return to Washington until Tuesday afternoon, meaning the earliest that shuttered federal departments and agencies could reopen would be Wednesday.

If the shutdown is still in effect Wednesday, that would mark its 19th day, making it the second-longest on record.

House Speaker Nancy Pelosi, D-Calif., said Saturday that House Democrats would introduce bills next week to fund parts of the government that are currently part of the shutdown, including the Treasury Department and IRS.

"This action is necessary so that the American people can receive their tax refunds on schedule," Pelosi said. "The certainty of the tax returns of hard-working families should no longer be held hostage to the president’s reckless demands."

The IRS has categorized issuing tax refunds as a "non-excepted" activity — meaning those tasked with processing refunds would be furloughed during a shutdown and millions of Americans wouldn't get their checks on time.

While the measure could help relieve some pressure from both lawmakers and the White House, it's unclear if the idea would be welcomed by Republicans. A spokesman for Senate Majority Leader Mitch McConnell's office, in response to a question on whether this would be considered for a vote, said "there would be no more votes on this issue until an agreement was reached between Republicans and Democrats in Congress that the president would sign."

The White House didn't comment on the possibility of the bills.

The shutdown began on Dec. 22, when nine federal departments and several smaller agencies – representing a quarter of the federal government – ran out of money and had to close their doors because of a budget dispute between the White House and Congress. Some 800,000 federal employees have been forced to go on unpaid leave or work without pay.

The sticking point has been Trump’s insistence on $5 billion in funding for a border wall. Democrats are refusing to give him the money, arguing that a wall would be expensive, wasteful and ineffective.

Currently, in its 16th day, the shutdown is now tied for the third longest, which happened in 2013 when President Barack Obama was in the White House. That shutdown started over a fight over the Affordable Care Act, also known as Obamacare.

Republicans in Congress sought to delay or defund the act after failing in their efforts at outright repeal. They attempted to force Obama’s hand by approving a temporary measure that would fund the government but would cut funding to implement Obamacare.

The Senate, controlled by Democrats, rejected the plan. The resulting impasse shut down the government. The standoff ended when Republicans conceded defeat and a deal was worked out to reopen the government. Polls showed that Republicans took the brunt of the blame.

The longest government shutdown on record lasted 21 days, and lasted from Dec. 5, 1995, to Jan. 6, 1996. The battle involved a dispute between President Bill Clinton and Republican House Speaker Newt Gingrich over spending cuts. That shutdown ended when the two sides agreed to a seven-year budget plan with some spending cuts and tax increases.

Late Thursday, on their first day back in the majority, Pelosi and House Democrats pushed through a package of spending bills to reopen the government. But in the GOP-led Senate, McConnell dismissed the legislation as “political theater, not productive lawmaking” and said he would not put the package to a vote because Trump would not sign it.

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Contributing: William Cummings