The White House has directed the Army Corps of Engineers to "look at possible ways of funding border security," Press Secretary Sarah Sanders told Fox News on Thursday night, as the ongoing partial federal government shutdown over money for a border wall is less than two days away from becoming the longest in the nation's history.

Separately, Fox News is told the White House directed the Corps to examine the February 2018 emergency supplemental, which included disaster relief for California, Florida, Texas, and Puerto Rico, among other states, to see what unspent funds could be diverted to a border wall, according to a congressional aide familiar with the matter.

Such a move still could require the president to declare a national emergency in order to access those funds to build a wall, because they were earmarked for a different purpose. The discussions with the Corps suggest the White House is closely looking at the possibility of declaring such an emergency, as Trump has floated repeatedly in recent days.

Sanders said Trump has not met with the Corps to discuss the matter.

Approximately $13.9 billion is available from the congressionally approved February 2018 supplemental spending bill, intended to cover natural disasters, and much of the available money comes from flood control projects, Fox News is told. The Military Construction appropriations bill could provide additional funding in the event of an emergency declaration.

Earlier Thursday, Trump told reporters, "I have the absolute right to declare a national emergency" and that, "if this doesn't work out...I would almost say definitely.”

The president, before and after his election, promised that Mexico "is going to pay for the wall." On Thursday, Trump -- reiterating a familiar argument in recent weeks -- said the favorable trade terms in the United States-Mexico-Canada Agreement (USMCA), signed last year but not yet law in the U.S., effectively fund the wall and fulfill that promise.

"When I say Mexico's gonna pay for the wall -- do you think they're going to write a check?" Trump asked. "No, they're paying for the wall in a great trade deal."

Texas Republican Sens. Ted Cruz and John Cornyn, speaking at a news conference after President Trump's visit to McAllen, Texas, later in the day, charged that the progressive wing of the Democratic Party was to blame for the partial shutdown and that no compromise seemed likely as a result.

"I think the president came down, number one, to listen -- to listen to law enforcement, to listen to Border Patrol -- but also to highlight the need for border security," Cruz told reporters. "Border security used to be in Washington an area where you find bipartisan agreement. It still is in Texas. Unfortunately, in Washington, we're in a different environment."

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Cruz added: "The objection of Senate Democrats' to the president's proposal is not a substantive objection. "This was $5.7 billion for border security, including a physical barrier. Both Schumer and virtually all of the Senate Democrats preivously voted for $40 billion for border security, including a physical barrier."

Schumer and other Democrats, including then-Sens. Barack Obama and Hillary Clinton, supported the Secure Fence Act of 2006, which authorized the construction of some 700 miles of fencing at the border. As of 2015, virtually all of that fencing had been completed, according to government figures.

"Both Schumer and Pelosi feel captured by the extreme left of the Democratic Party, and so they have forced the shutdown," Cruz added.

Cornyn, Texas' senior senator, said security experts backed the need for a wall.

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"Yeah, in some places we do need a physical barrier, because that's what the experts tell us -- that's what the Border Patrol tells us," Cornyn said. "I, for one, would rather listen to the experts than the politicians in Washington, D.C."

Meanwhile, Democratic senators and union leaders led federal workers in rallies at the White House and across the country on Thursday, just one day before the partial shutdown over border wall funding threatens to deny all of them their first full paycheck.

Roughly 420,000 employees were deemed essential and have been working unpaid. An additional 380,000 were staying home without pay. On Thursday afternoon, after assurances from Senate Majority Leader Mitch McConnell, R-Ky., that President Trump would sign the bill, the Senate passed legislation to provide back pay for furloughed federal workers.

Statistics provided by the Labor Department showed 4,760 federal employees filed for unemployment benefits in the last week of December, an increase of 3,831 from the 929 who applied the week before.

"Shutting down the government is not a policy that should be followed," House Majority Leader Steny Hoyer, D-Md., told a boisterous crowd of protesters in Washington, D.C., on Thursday. Some near the White House chanted, "Do your jobs, so we can do ours."

Some disagreement about the way forward was apparent among top Republicans on Thursday. South Carolina Republican Sen. Lindsey Graham, in a statement, urged Trump to declare a national emergency to build the wall, saying House Democrats were refusing to negotiate reasonably. Sources told Fox News that Trump earlier killed an effort by Graham to end the shutdown with a potential compromise.

“I would advise against that as a bad precedent, even if the president's got the authority to do it," Sen. Chuck Grassley, R-Iowa, told Fox News. "I’d advise against it, and I’d think that each side ought to be laying something on the table to negotiate.”

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Should the White House move forward with an emergency declaration, it has a handful of legal routes to take. The National Emergencies Act grants the president broad authority to declare emergencies, and several federal laws then could clear a path for the White House to move ahead with building a wall.

One statute, 33 U.S. Code § 2293 - "Reprogramming during national emergencies," permits the president to "apply the resources of the Department of the Army’s civil works program, including funds, personnel, and equipment, to construct or assist in the construction, operation, maintenance, and repair of authorized civil works, military construction, and civil defense projects that are essential to the national defense."

Another law, 10 U.S. Code § 2808 - "Construction authority in the event of a declaration of war or national emergency," permits the secretary of defense, in a presidentially declared emergency, to use "funds that have been appropriated for military construction" for the purpose of undertaking "military construction projects."

Fox News' Chad Pergram, Alex Pappas, John Roberts and Mike Emanunel contributed to this report.