I've had similar problems traveling on official business in the past.

Typically, Once it becomes clear that I cannot get a room at the Gov't rate, I'll wait until the day prior to travel. At this point many managers will be willing to let the unsold rooms go at a discounted rate...maybe not the government rate, but at least something realistic.

My experience has been that they will not feel any pressure until "late in the game."

Another avenue for your coworker: Most government agencies recognize that government rates are not always available to travelers on official business. They usually have procedures in place to pay for higher rates due to lack of available government rates. Admittably, this can be a painful process, but worth the effort. if you go that route....make the reservation now to ensure a oom is available, then continue to look/egotiate for a government rate.