I think that is wrong; I think they did have the votes to override him. I may be wrong, but I might have even read that on this very thread.
Two thirds majority to override, vote in house was 252 for, 167 against. Two thirds would have been 279 for. So not only would the veto not have been overridden, I would be willing to bet some of the 252 fors would have changed to against. So once again, Bush signed a bill he knew was unconstitutional even though he knew a Veto would not be overridden.
But at least he could have retained his honor and oath by vetoing it.
House
On passage Passed by recorded vote: 240 - 189 (Roll no. 34).
Senate
Cloture on the measure invoked in Senate by Yea-Nay Vote. 68 - 32. Record Vote Number: 53.
Passed Senate without amendment by Yea-Nay Vote. 60 - 40. Record Vote Number: 54.
55.94% in House (not veto proof) 605 in Senate (barely veto proof, if no one changed their vote after a President of their party vetoed the bill, but that's speculation)