I recently have gone through the interview process with a company where I mentioned a range for what I was expecting. This was stated to me to be a full time position. At the end, they offered me lower than my minimum range and a three month contract to boot. Do I just come back to them and say "look, my lower end of the range is higher than your offer, can we make that work?" I'm sure they'd come back and say "how about we revisit after your contract is over."
Be firm about your minimum salary and explain why it is fair and stick to it.