I've done something similar several times, going nearly direct between TUS and ABQ in a 182. It's been a few years (last trip was to intercept the total annular eclipse) but typically there'll be a 50-mile stretch where you lose flight following, and they have to give you the next frequency very early.
If there is strong turbulence, or clouds prevent VFR, the airways route that takes you over Socorro, Truth or Consequences, etc. might be better, which I've done a few times also.