Bureaucratic organizations like governments can have almost all of their budgets encumbered year to year in doing what they have already been doing. For established vendors, this momentum and longevity can be a boon in that it leads to long customer relationships. For startups, it can present a problem.
How do I break in with a new solution and get the organization to spend money on a new category of service or software?
One solution is to find a consulting budget. If there is a recurring need to hire outside expertise for a particular kind of task that can be automated with software, then you can tap into that budget.
For example, Remix did a great job of this early on by doing public transit planning for cities. the software replaced an expensive recurring consulting project that cities were used to spending money on and improved their ability to do it more often and with a tighter turn around times. They were able to expand customer relationships from there.