I suppose it depends on what you'd hope to get out of a program like that, in terms of your goals and expectations.
About the shortest time frame you could do an MBA is one year, and one-year MBA programs are relatively rare in the US. Schools like USC, Cornell - Johnson, Pittsburg - Katz, Kellogg... These schools offer one-year MBA programs, but be advised that they are for a particular kind of student: those who don't want to make large shifts in their career.
Other, shorter options might include a general management program: Harvard's GMP is delivered in four modules, both on-campus and off, over the course of five months. Columbia's General Management Leadership Program is less robust, but also less costly and time-consuming: it's only one two-week long module. Good program though.
For public administration focused courses, there are a number of shorter executive programs that you could potentially mix and match in order to surgically target your needs. For instance, the Brookings Institute offers a number of policy-type programs, one- or two-day type deals, many of which are aimed at federal employees, but some are more general. Here's a listing of those:
http://www.nextexecutive.com/topics/government-public-administration