Before talking interest rate we have to figure out WHAT we are doing. What type of loan do you have now, what rate are you at now...that would make a difference in whether a refi even makes sense to do.
FHA is a great loan but it introduces monthly mortgage insurance. On your loan, the MI on an FHA loan is about $110 per month which could completely mitigate your savings. If you already have an FHA or VA or Rural loan, I would look first at a "streamline refinance" that does not involve income documents or an appraisal.
If your loan is currently "owned" by Fannie Mae or Freddie Mac and you don't pay MI now, I would look to using the HARP program...a special program that is part of the economic stimulus package. I can look that up by property address on the Fannie or Freddie website. This program accepts a 650 score.
With this information I can properly quote rate/closing costs/APR and can also advise whether it makes sense to do.