Can a US citizen travel to Myanmar from Chiang Mai to obtain a 60-day visa?

It takes staying overnight.

You turn in your paperwork and passport in the morning of one day and you get it back with the visa in it the afternoon of the next day.

You can FLY to Yangon and apply for a single entry tourist visa at the thai consulate there for 40USD (they only take US dollars at the consulate).

That visa would get you stamped in for 60 days when you come back to thailand and you could extend it by 30 more days at the immigration office if you needed to for 1900baht.

OR

You could just go to the Mae Sai - Tachiliek border with burma, stamp out of thailand, stamp in&out of burma (for 10USD or 500baht) then stamp back into thailand to get a 30 day visa exempt entry stamp which you could also extend for 30 more days at the immigration office for 1900baht if you needed to.