Initially he might have thought, "well, I can't admit that because I would sound so callous, and no one will ever believe I had anything to do with her disappearance anyway, so I'll just stonewall."
This, to me, is a possible scenario wherein Condit didn't have anything to do with Chandra after a date certain (say the 24th if that's when the records stop), and had nothing at all to do with her disappearance.
Do I believe it? No. It is inconceivable to me that he would continue to stonewall, allow his children to lose their high-paying jobs, subject himself and his wife to the implacable scrutiny of the media following them 24/7 if he had nothing to do with Chandra's disappearance.
But Gary Condit has proved that he is no "rocket scientist." In fact, he seems to be uniquely stupid for someone in elected office. Way back in college I read an existential novel (Camus' "The Stranger" I believe) where someone who had no connection with his mother's death allows himself to be thought guilty of it due to essentially his inertia and ennui -- a total unwillingness to exert himself enough to fight back because he couldn't conceive that people would actually think him guilty of something he did not do. Could Condit be a Camus-like figure?
At any rate, this is more of a "thought experiment" than anything I could actually believe because I truly believe that Condit is 100% GUILTY!