No problem with an electoral tie. The House of Representatives then gets to elect the President from the three candidates with the most electoral votes, and they keep voting until someone is elected.
As for some other scenarios. . .
In 2008, it took something like 7 months to finally resolve the Franken-Coleman senatorial election in Minnesota, but it did eventually get resolved.
The New York City mayoral primary was supposed to take place on September 11, 2001. It was delayed two weeks.
In 2000, Missouri’s Mel Carnahan died too late to be replaced on the ballot for the Senate election. He won, anyway, and the Governor appointed his replacement.
Recall that in 1841 William Henry Harrison died only one month into his term. The office of President had never been vacant before, but John Tyler managed to be accepted as legal successor without causing a palace coup.
And for some absolutely unexpected, bizarre scenario that no one could possibly take into account – like the 2000 presidential vote in Florida – it winds up in the court system.
TLDR: We fake our way through it.