Nearly three weeks after the start of the government shutdown, Republicans are expressing optimism that Senator Chuck Schumer will soon relent and allow a funding deal to pass after this weekend’s “No Kings Day” protests. The GOP has long argued that the shutdown is not about policy, but rather about Mr. Schumer’s own political standing. 

Monday marks the 20th day of the total government shutdown, making it the third-longest government funding lapse in American history. With Democratic voters beginning to feel the pain of lapsed services, mass layoffs, and cuts to projects in blue states, Republicans believe they can clinch the five extra Senate Democrats needed to reopen the government. 

Speaking to reporters at a press conference on Monday, Speaker Mike Johnson said he believed Mr. Schumer will come to his senses. The speaker argues that the Senate Democratic leader was only trying to wait out liberal activists planning a nationwide anti-Trump protest Saturday. 

“Over the weekend, we saw what it was all about. The Democrats made crystal clear that this is about politics. The politics were on full display. The politics — the spectacle — is what the mobs, the crowds, [and] the rallies this week were all about,” Mr. Johnson said of the No Kings protests. “This shutdown is about one thing and one thing alone: Chuck Schumer’s political survival.”

The group primarily responsible for organizing the protests, Indivisible, has been pushing Democrats for months to more aggressively stand up to the president. Mr. Johnson cited comments the group’s co-founder, Ezra Levin, made in an interview with NBC News ahead of the protests.  

“My main message to them is: The cavalry is coming in on October 18 and they’re either going to be celebrating you or they’re going to be calling for new leadership,” Mr. Levin told the outlet. 

“That’s a direct threat to Chuck Schumer, and he heard the message,” Mr. Johnson said of the comments. “Now that Chuck Schumer’s had his spectacle, he’s had his big protest against America … [everyone] should be hoping that he is finally now ready to go to work and end this shutdown.”

Senate Democrats have so far voted 10 times to block the funding proposal from coming to the floor. It requires 60 votes to break the filibuster and advance the bill. So far, just three Democrats are supporting the legislation, while one Republican is opposed, meaning that if all other lawmakers hold steady in future votes, Republicans will need five Democrats to vote to advance the bill. 

“Now that their ‘Hate America’ rally is over, I hope that at least five Senate Democrats will finally do the right and responsible thing by breaking ranks with Chuck Schumer, passing our clean [funding bill], and reopening the government,” the majority whip, Congressman Tom Emmer, told reporters at the press conference. 

The White House is expressing optimism similar to that of its friends on Capitol Hill. During an interview with CNBC on Monday morning, the director of the National Economic Council, Kevin Hassett, predicted that the shutdown would likely end this week. 

“A lot of our friends in the Senate have said that it was just bad optics for Democrats to open the government before the No Kings rally, and that now there’s a shot that this week things will come together and very quickly the moderate Democrats will move forward and get us an open government,” Mr. Hassett said. 

He mentioned comments on Friday from Senator Jeanne Shaheen, a Democrat from New Hampshire, who is talking with Republicans about a path out of the shutdown. Ms. Shaheen, who is retiring next year, told the New Hampshire Bulletin that while leadership is not yet involved, there are talks going on about how to open the government while guaranteeing that there are negotiations later this year about extending some enhanced Affordable Care Act subsidies. 

Mr. Hassett, who called Ms. Shaheen a “friend,” told CNBC that her willingness to work with Republicans is a sign that there are “cracks in the Schumer armor.” Ms. Shaheen has been voting with the vast majority of her Democratic colleagues to block the funding bill, and many view her as one of the first possible dominoes to fall should a band of moderate Democrats break with Mr. Schumer. 

“I think the ‘Schumer Shutdown’ is likely to end sometime this week,” Mr. Hassett said.