Not the Senate. That takes 60 votes to end the democrat's filibuster, which is why the last dozen attempts by republicans to pass a clean CR with no changes to the current budget failed. (The last one yesterday[1] failed with 54 in favor 44 against. Three democrats voted with the republicans in that vote, still not enough.)
[1]: https://www.aha.org/news/headline/2025-10-03-senate-again-fa...
Not having supermajority doesn't mean they aren't in control. The fact is, the president could say one sentence, and the shutdown would be over. It's no surprise that the last 2 record setting shutdowns happened under this president.