Thanks for the links Dave
For the I70/Hwy 40 Route
According to what I could see on the Utah site (2nd one Dave listed), the only road construction planned for Hwy 40 is in August so that should not be a concern. I checked CDOT's Construction Map
and I don't see anything of concern other that some roadwork in Silverthorne. Looks like it should be relatively clear sailing
For the I80 route
Well, you should probably look for yourself if you are going that way. Looks to be a couple sections (about 10 miles total) in Western WY where I80 will be down to one lane and speeds reduced to 10mph.
Aside from this, the only thing I saw was construction in Wendover listed.