A lot of states have already passed similar laws and are merely waiting on the Federal law to come into effect. So it's likely to become law soon.
What is the federal government's role in this? Can a state ignore this (almost) law and do DST anyway?
Yes
> Will the president veto it?
No
> When can I literally set my clock to this?
2023 at the earliest, but probably much later, if ever. The legislative process is not known to move quickly.
Also, IIRC, bills must originate in the House, which makes me think something like this has already passed there at some point.
> Also, IIRC, bills must originate in the House
Only those related to revenue
Now that the Senate's passed it, I think there'll be enough momentum for the House to take it up relatively soon.
[0] https://constitution.congress.gov/constitution/article-1/#ar...