The PubMed website, which can be so useful to us, is a part of the National Library of Medicine (NLM), and that in turn comes under the National Institutes of Health (NIH). That is, all are directly funded by the US Government.
If, as many expect, the US fails to get a budget passed, and the stopgap funding bill has just failed, the websites that are part of the NIH might well closedown. This has previously occurred in broadly similar circumstances. They might close immediately, or keep going for a while, or simply not have any maintenance performed for the duration. No new papers. No fixes if it fails.
Very difficult to predict exactly what will happen.
Even if PubMed becomes totally inaccessible, we might have an alternative. The European Union’s similar Europe PMC. The “might” is simply that it could become overloaded.
Being designed later, it has some good design features. For example, the PubMed Central database of actual papers is embedded within the same system. In some ways, I do prefer it to PubMed and PMC separately.
Have a look here – even if PubMed is unaffected!