PhD Public Policy with Lower Level Institutions

[Mpelosi]

A little background about myself. I graduated with a Masters degree at SNHU in Applied Economics with a 4.0 GPA. I'm currently enrolled in the JHU MS Government analytics program. My long term goal has always been to obtain a PhD in public policy. 

But I also know that the prestige of my previous institutions is pretty lackluster. I've done every single free/volunteer/consulting/paid public sector job possible. 

I am curious if anyone has gone to lackluster institutions and still got into a good PhD program in policy / government. 

It's difficult to find people in similar situations, so I'm casting a conversational net. 

My top pick is the Brandeis PhD in social policy if that helps at all. My research focus is poverty analysis and time series modeling  

thanks in advance for any help.

Sincerely,

Mike