Joe Biden knows that a government shutdown could hurt many people. Fortunately for him, these people include Republican members of the House. Consequently, Biden is not going to help Speaker Kevin McCarthy (R-CA) by asking House Democrats to bail the Speaker out. In fact, a government shutdown might well help the Democrats in 2024 by letting them campaign on: "Republicans are not capable of governing. All they can do is fight with each other." That is a message most voters can understand.
Also important is that Biden and McCarthy made a spending deal in May, one that the Freedom Caucus never liked and is trying to kill. Biden is effectively telling McCarthy: "If you can't live up to the deals you make, how can I ever negotiate with you again? Your word apparently means nothing at all." Biden is also talking about how the cuts the Freedom Caucus wants go against things the other Republicans (and Republican voters) want. For example, Biden said that the FC-approved budget will require firing 800 Customs and Border Protection agents. Democrats would love to campaign on: "Republicans are weakening border security by reducing the number of Border Patrol agents."
However, Biden is supporting a bipartisan budget bill in the Senate that adheres to the deal Biden and McCarthy made in May. When it becomes clear that McCarthy can't get anything through the House, the pressure on everyone to simply accept the Senate bill will increase. If all the House Democrats support the Senate bill, it will take only five Republican defections to pass it through the House.
Biden's thinking, obviously, is that House Republicans would be blamed for a government shutdown. He could be wrong, but he has the bully pulpit and they don't. So for the moment, he is staying out of it and letting McCarthy fight with his own caucus. Republican senators very much think their party will get blamed if National Parks close and passport processing is even more delayed come Oct. 1. For example, Sen. Kevin Cramer (R-ND) said that government shutdowns "always seem to get blamed on Republicans." A Republican senator who wished to remain anonymous said: "When you have a Democratic Senate and a Democrat for president, I don't know what they [the FCers] think they're going to be able to accomplish. Maybe it's one of these things where it has to be experienced."
This is why Republican senators are on top of the situation and may encourage Minority Leader Mitch McConnell (R-KY) to join with Majority Leader Chuck Schumer (D-NY) and pass something, even a continuing resolution to keep funding the government for a couple of months, and send it over to the House with an ultimatum to vote yes or else. Normally, the House moves first on spending bills, but there is nothing in the Constitution preventing the Senate from going first. In contrast, tax bills must originate in the House because Art. 1, Sec. 7, Clause 1 says: "All Bills for raising Revenue shall originate in the House of Representatives." Both chambers may originate spending bills, though, and Senate Republicans may decide to break with tradition and go first this time.
One way out for McCarthy is to make a deal with Minority Leader Hakeem Jeffries (D-NY). This would probably result in two things. First, the bill would pass, mostly with Democratic votes. Second, Rep. Matt Gaetz (R-FL) would introduce a motion to vacate the chair. At that point Democrats would be on the spot. If they all voted to fire McCarthy, the resulting chaos would make for great television ads in 2024 under the heading: "Republicans can't govern." What is very important is for Democrats to stay unified and vote as a bloc. If the leadership decides to embarrass McCarthy, all the Democrats need to follow suit. Their "reason" could be that McCarthy made a promise to Biden in May and then broke it. That makes him unworthy to be speaker. Of course, they would greatly enjoy another 15 rounds of voting followed by McCarthy being elected speaker again.
Any goodwill McCarthy might have had with the Democrats vanished when he decided to allow an investigation of Joe Biden to start—especially when he knows the votes to impeach Biden aren't there and the last time the Republicans tried this stunt (in 1998) it backfired in their faces. House Democrats would now love to see McCarthy flail and fail. (V)