You have not provided enough information for a intelligent answer.
First of all, a QUALITY 600w psu with FOUR 6-pin 75w connectors would likely be plenty for 2-6870, depending on the rest of your system components, which you failed to mention.
Second of all, a CHEAP 600w psu only puts out a real 400w. A QUALITY 600w psu, will put out a true 600w.
Since you didn't mention the power supply by name, I'm assuming it's a CHEAP unit and it probably doesn't even have FOUR 6-pin connectors. let alone a real 600w of output.
So the answer is no.