Originally Published: 01 AUG 22 12:43 ET

By Sonnet Swire, CNN

(CNN) -- Comedian Jon Stewart and veterans' advocates on Monday called on senators to stay overnight when they return to Capitol Hill to pass a stalled bill aimed at expanding health care access for military veterans who became ill after being exposed to toxic burn pits.

"They're allowed to stay open past five," Stewart said on the US Capitol steps Monday morning, joining burn pit protesters who have remained there over the weekend as the bill remains in limbo. "So my suggestion to this Senate would be when you come back, if all the members aren't here, keep the lights on. Keep the doors open. And don't leave here tonight, until you do the right thing by these folks."

While Senate Democrats voted unanimously for the measure last week, Republicans voted against a procedural step to advance the legislation, effectively stalling the Honoring Our PACT Act, which aims to provide assistance to veterans who have become ill after being exposed to burn pits during their military service.

Matt Zeller, a major in US Army Reserves and senior adviser for Iraq and Afghanistan Veterans of America, also told CNN's Kate Bolduan that Republicans should move to support the PACT act now, with no time to waste.

"We're going to stay here until this gets done because we're doing this for the people who have died. We're doing this for the people who are dying," Zeller said. "And we're going to do this most importantly for the people who will die if we don't do this now."

A new vote is expected to occur early this week but not Monday night, according to a senior Democratic aide familiar with the matter.

Senate Majority Leader Chuck Schumer plans to bring the procedural vote -- which requires 60 senators to advance -- back up to consider early this week and offer two amendments sought by Republican Sen. Pat Toomey of Pennsylvania for a vote at a 60-vote threshold. If Republicans accept that offer, it could pass early this week -- though any one senator can object and slow the process down.

Stewart has knocked the GOP for holding up the bill's progress and for misinterpreting the proposal. He traded online barbs with Republican senators' newfound opposition to the bill that they both voted for in June.

On Monday, Stewart addressed the feud.

"You can attack me all you want, and you can troll me online," he said. "But here's the beautiful thing. I don't give a shit. I'm not scared of you. And I don't care. These are the people that I owe a debt of gratitude to and we all owe a debt of gratitude to, and it's about time we start paying it off."

"Can we please not force veterans, disabled from their heroism and sacrifice, to stand outside the Capitol building, days on end, waiting on this Congress to do the thing they already did on June 16? It passed 84 to 14. Nothing changed in it," Stewart said Monday.

He added: "Ask any senator, any one of the senators that changed their votes point to the section of the bill that changed that made your vote go from desk to no point to the section of the bill that's filled with pork point to the section of the bill that is not being spent on veterans. You won't because you can't because it's not there."

Toomey was one of a few Republicans who voted to block the bill designed to help US military veterans exposed to toxic burn pits. He defended his vote Sunday on CNN's "State of the Union," saying he blocked the bill because of an accounting provision in the language.

Toomey said the bill as written would "allow our Democratic colleagues to go on an unrelated $400 billion spending spree." He has said he wants a vote on his amendment to change the spending categorization before he agrees to allow the bill to come to a vote. It's unclear as of early Monday whether Schumer's proposal will be enough to assuage Toomey's concerns.