(NewsNation) — Senators expect to reach an agreement that will win enough GOP support to pass contentious legislation to aid military veterans exposed to toxic burn pits, according to NewsNation sources on Capitol Hill.

The PACT Act would enable additional health care coverage for more than 3 million veterans who were exposed to dangerous chemicals from burn pits while serving overseas.

Senators and aides who talked to NewsNation said they expect to iron out their differences this week.

Veterans outside the Capitol say they don’t care what the process looks like as long as the bill gets passed.

Dozens of veterans have been taking shifts camping outside the Capitol — sleeping on the steps — refusing to leave until Congress passes a bill giving vets with cancer the same health benefits as veterans injured in combat.

Standing outside the Capitol on Sunday, Kimberly Hughes was expecting a celebration this week. Instead, the blockage of the bill took Hughes’ back to when her late husband, Maj. Gary Hughes, was denied health coverage.

“It was like I relived that day last Thursday,” Hughes said. “I was heartbroken. It was devastating to have to go through all of that again.”

Hughes, whose husband served for 27 years and was deployed to Iraq and Afghanistan, called on senators to quickly pass the legislation. She said the veterans’ groups wouldn’t stop until the bill gets across the finish line.

“All of us here … they were not trained to quit,” she said. “They were trained to fight, and they’re going to keep on fighting.”

Navy and Air Force veteran Nathan Kempthorne emphasized that if the bill doesn’t pass, it will impact veterans’ survivors, too.

“If this bill does not pass and these folks die of these cancers, their spouses and their dependents will get nothing,” Kempthorne said. “They are creating a multi-generational trauma for all of these families.”

Many veterans exposed to toxic burn pits while serving overseas develop cancer later in life, and advocacy groups have been fighting to get those vets extended health benefits for years.

Veterans who have been exposed to dangerous chemicals in burn pits while on duty can suffer from devastating health conditions including neurological disorders, pulmonary diseases, rare forms of cancer and many unexplained symptoms. Some of those diseases are so serious that they lead to death.

Last week, they thought their fight was over.

Congress was poised to pass their bill, but at the last minute, 25 Republican senators changed their votes from yes to no. They blamed Democrats for including a budget gimmick that could divert billions away from veteran issues.

Democrats and veterans’ groups say that’s not true. They point out the bill is virtually the same as it was when, just a few weeks ago, Republicans overwhelmingly supported it.

They say Republicans are playing politics.

Sen. Pat Toomey (R-Pa.) on Sunday defended his “no” vote on the bill against what he called “false accusations” from comedian and former “Daily Show” host Jon Stewart.

Stewart slammed Republican senators after they blocked the passage of the bill, saying, “Their constituents are dying.”

“We’re gonna get it done. … You don’t tell their cancer to take a recess, tell their cancer to stay home and go visit their families,” Stewart said. “This is a disgrace.”

Toomey, during an appearance on CNN’s “State of the Union,” called Stewart a “pseudo-celebrity” and accused the bill’s Democratic backers of “the oldest trick in Washington.”

“People take a sympathetic group of Americans — and it could be children with an illness, it could be victims of crime, it could be veterans who’ve been exposed to toxic chemicals — craft a bill to address their problems, and then sneak in something completely unrelated that they know could never pass on its own, and dare Republicans to do anything about it,” Toomey said.

Toomey insisted that Republicans don’t oppose the bill itself, but are worried about Democrats using it to acquire funds for unrelated matters.

“Republicans are not opposed to any of the substance of the PACT Act,” he said. “What I’m trying to do is change a government accounting methodology that is designed to allow our Democratic colleagues to go on an unrelated $400 billion spending spree.”

The Hill and the Associated Press contributed to this report.