I applied to the Legislative Affairs program. While visiting DC, I met with the director of the program. He said that while it's built for working professionals, some people come straight from undergrad to their program. Typically, they look for people with work experience (~3.5 years, preferably in a supervisory role). I asked if I would have to do master's work en route to a PhD in Political Science/Public Policy later on if I did this program, he said it wouldn't affect it.
I'm excited about the program, though I may be deferring for a year to do a 1 year MA at another school. Hope that helps.