Shopping based on a monthly payment is the last thing you should do. Negotiate the final price or price differential if you have a trade, and then see what they offer for an interest rate. It's a good idea to know what you can get from your credit union or bank too because it can be a bit better. There was a cash incentive to finance through Chrysler when I bought my truck and I think the rate they offered was 1.9%, so I did that initially and then did a no-cost refinance through our credit union at .9% within about a week. Obviously you need to review the specific loan documents you sign to be sure there aren't any restrictions or penalties involved.
I would also recommend price shopping any high volume dealerships in your region. Try to get the local guys to price match but be willing to travel if they won't.