By Deborah Gembara

WASHINGTON (Reuters) - Hundreds of furloughed federal employees chanting "We want our pay!" marched on the White House on Thursday, the 20th day of a partial government shutdown over U.S. President Donald Trump's demand for border wall funding.

"Stop the shutdown!" protesters shouted in the bitter cold at the union-organized demonstration that started at the AFL-CIO headquarters and ended in front of 1600 Pennsylvania Avenue, where they hoisted signs reading "Trump: End the Shutdown" and "Not a strike - we want to work."

Some 800,000 federal government employees have been ordered to stay home or work without pay during the shutdown brought on by a standoff between Trump and Democrats in Congress over Trump's demand for $5.7 billion to build a wall on the southern U.S. border with Mexico.

Trump, in a 2016 presidential campaign promise, repeatedly vowed that Mexico would pay for the wall. But he has said he will not sign any bill to reopen the government that does not provide wall funding.

Elaine Suriano, 62, a furloughed scientist with the Environmental Protection Agency, said she would have to dip into her retirement savings if the shutdown continued and robbed her of yet another paycheck.

"It's just clear that this administration doesn't understand normal people and real life or they wouldn't do this," Suriano said.

In its third week, the shutdown of about a quarter of the federal government is the second longest since the mid-1970s. Trump has said it could continue for months or even years.

Many furloughed federal workers have turned to online fundraising outlets such as GoFundMe.com to help cover expenses from food to utility bills.

Mathew Crichton, 32, a furloughed Peace Corps employee, said uncertainty over how long the shutdown will last made it impossible to budget for food, lodging and other needs.

"It could go on another day, and it could go on more weeks. It could go on for months," Crichton said. "It's really a shame that I'm ready to go to work. I'm able to go to work and I can't."

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Protesters, many wearing neon green vests reading, "I am a worker. I demand a voice," on Thursday demanded the government be reopened, separate from any debate over wall funding.

Smaller protests across the country – from Palm Beach, Florida, to New York City - had similar demands. In Ogden, Utah, dozens of out-of-work federal employees gathered to urge an end to the shutdown, some holding signs reading “I am TSA. I am furloughed. I am not a pawn. I’m a voter” and “800,000 unemployed. Hurts our family and our economy.”

Trump was not at the White House when the protesters arrived, having traveled to the U.S.-Mexico border in McAllen, Texas.

The president has said he has the right to declare a national emergency if no deal with Congress can be reached on funding the border wall project.

(Additional reporting by Katharine Jackson in Washington and Barbara Goldberg in New York; editing by Bill Berkrot)