40 days and 40 nights should be plenty of time -
But watch out if you see the waters rising.
Working backwards, you will be riding in Texas in early July. Uggghh!
But most of the rest of your riding will be nice if you stay fairly high.
(Of course, Colorado now has multiple definitions of that term.)
Accessing most metro areas - except places like Portland - can be tough.
Is Salt Lake City a definite destination? Some tough touring on the Wasatch Front.
The way I count it - it's usually about 2 weeks Portland to San Fran -
Then another two weeks to central Utah via the Western Express route.
(You can ride via Yosemite, Tonopah, and Caliente, too.)
So that gives you about a week to ride from central Utah to Taos, NM.
Then another week to hightail it to Austin.
On the Pacific coast most Oregon and Calif parks have cheap hiker/biker campsites.
You can camp anywhere on federal land in Nevada/Utah for free outside of National Parks.
Plenty of free camping in the national forests of Colorado and northern NM.
And small towns (not big towns) in west Texas are usually very generous letting you camp in the park.
Avoid microbreweries and women in fishnet stockings in the evenings and you should be fine $$$-wise.