Comedian and activist Jon Stewart says the fight is not over for 9/11 first responders after the House of Representatives passed legislation Friday to extend funding for the September 11th Victim Compensation Fund until 2090.

"Passing this in the Senate in two weeks -- and we're going to hold (Senate Majority Leader Mitch) McConnell to his word -- will be a chance to exhale. But it doesn't fix the grief and the suffering that [9/11 first responders] will continue to experience going forward," Stewart told CNN's Alex Marquardt.

In June, Stewart accompanied a group of first responders and delivered an emotional plea to lawmakers about reauthorizing the fund. One of the first responders who made his case to lawmakers, Luis Alvarez, died a few weeks later at age 53 from complications due to cancer linked to his time at Ground Zero.

"We made, we forced, we shamed the process to work so Lou Alvarez's passing is not in vain," first responder John Feal said Friday, becoming visibly emotional.

"What [Lou] really wanted was to see this happen before he passed, and we weren't able to make that happen, but in his memory, we're going to be able to make it happen in the Senate," Stewart said.

The bill easily passed the House by 402-12 and will now be sent to the Senate, though the timing of that vote is not yet known. McConnell met with first responders, including Feal, at the end of last month, after which Feal told reporters that the Kentucky Republican had committed to holding a vote to extend the fund.

Stewart, who has been deeply critical of Congress' role in advancing the bill, ripped lawmakers for failing to attend the committee hearings about reauthorizing the fund in June. When McConnell said in an interview that members' absence at hearings "frequently happens because members have a lot of things going on at the same time," Stewart responded in a surprise appearance on "The Late Show with Stephen Colbert."

"Now I feel stupid," Stewart said sarcastically. "This is a huge misunderstanding. I didn't know that they were busy. ... I didn't mean to interrupt them with their jobs!"

Stewart referenced the justification that members were too busy in June again Friday.

"Well, Lou Alvarez chose to spend his last few weeks on Earth fighting, not for himself, but for the other families and victims. His time -- Lou's time -- was the most valuable time," Stewart said.

On Monday, lead sponsors of the fund announced that the legislation would be renamed to honor Alvarez and others. The bill will be called Never Forget the Heroes: James Zadroga, Ray Pfeifer, and Luis Alvarez Permanent Authorization of the September 11th Victim Compensation Fund Act.

"We're going to make sure that Mitch McConnell sticks to his word, and over the next week or two we're going to keep the pressure on the Senate," Feal said. "There's 27 members of the Senate that aren't on board. So I am giving you the next week to get on board, or we're going to make your life miserable."