MPP/MPAs are professional degrees; the best programs really stress professional experience. The students who come in straight out of college have to be stellar candidates in everything from LORs/SOPs to GPA/GREs, and usually with relevant internship/research experience.
I don't know how colleges consider taking an extra term, but it might be worth your while if you can get that internship. Personally, I'd advocate getting some professional experience for a year at least once you graduate--you mentioned doing part-time Americorps in school, so you might look into a full-time Americorps position to get experience in the issue area you want to study the policy for.
This is outside my discipline, but I have not encountered a graduate school that would look down on someone for taking more than four years to complete an undergraduate degree, especially since they can look at your transcript and see that you weren't failing out of classes or withdrawing in the middle of a semester or... any of the red flag things that might indicate a lack of commitment or seriousness. A lot of students go outside the traditional time frame for a lot of good reasons, and I think graduate admissions folks tend to understand that. That said, OregonGal is quite right to note that programs in public policy prefer students with relevant paid experience. Internships are nice. But it would be even better, both in terms of admissions and in terms of education more broadly conceived, to enter the professional world after you graduate and gain some job experience.
