Won’t their Governors just veto it?
They can’t.
“Won’t their Governors just veto it?”
An interesting question. Inasmuch as this election involves choosing Presidential electors, a case could be made that this falls under Article 2 of the US Constitution, which gives the state legislatures sole authority to determine how the electors are chosen. Under the Constitution, the Governor has no role in that process unless the Legislature gives it to him/her. So they could conceivably pass legislation stating that all votes for the presidential election must be received by the closing of the polls on election day and that the state courts have no jurisdiction to change that, and I don’t think the governor nor the state courts could do anything about it. In that case, the state courts could allow votes for state and local offices received after the deadline to be counted, and maybe even for Congress, but not for president.
Do bears poop in the woods?