It's the power supply's +12 Volt continuous current rating that determines whether or not it will work, not the power supply's total wattage rating.
The Dell Inspiron 545s 250W power supply has a +12 Volt continuous current rating of 17 Amps.
A reference clocked Radeon HD 6670 should be drawing less than 5 Amps from the +12 Volt rail under normal use.
That leaves you 12 Amps for powering the CPU, motherboard, hard disk drive motor, CPU cooling fan, case cooling fans, etc. which should be more than enough.
I've read of people using the Radeon HD 6670 in a Dell Inspiron 530S and Dell Inspiron 546s with the stock 250 Watt power supply and they did not have any problems with it.