According to that 5970s use 304W under maximum load. x2 is 608W. Then you have to add the rest of the system to that to know what your likely maximum power consumption will be.
But you definitely won't be overloading a 1000W PSU. The only question remains whether you feel comfortable stressing your PSU to the level that you will be doing.
If it is a high quality unit then you shouldn't necessarily be uncomfortable because a high quality unit can deliver its stated wattage all day.
Of course it depends on the PSU, do you already have it? If so what is the model name? If not then what is your budget and where are you buying from?
Do you have a budget for the case?
Listing some of your preferences for a case (besides fitting 5970s and other obvious things like 'good airflow') would be helpful in choosing some to recommend.