IBM is best at writing iron clad contracts that mean precisely that -- no matter the outcome, they get paid.
The problem is not lowest bid (which few government contracts are any more, AFAIK), but the fact that government contracting is its own domain of expertise (actually, often a separate domain for each state plus the federal government, and even many local governments) separate from the kind of work actually being contracted for, and there are in any field a very small number of players (compared to the field as a whole) that have developed expertise in the "winning government contracts" domain (and, in IT, IBM is one of them, at essentially every level of government.)
Of course you can pay more.
-- Oracle