If, hypothetically, Burr were to step down, there would be a special election for his seat ONLY if his resignation was effective more than 60 days before Election Day, that is, before September 4, 2020. If it's on or after that date, the special wouldn't be till 2022. https://twitter.com/DelWilber/status/1260751071762419713

We're a long ways off from any of that. But being served a search warrant by the FBI is not a comfortable place for anyone, let alone a US senator.

A potential effect of this development: when people discuss Burr they're likely to bring Kelly Loeffler back in the spotlight too.