A common expression coming from the Right portion of the media is that Senate Democrats are trying to Bork the nomination of John Roberts. So far, the opponents of the nomination have found nothing that sticks particularly well.
If you accept the word of the Drudge Report, then it would appear that the New York Times is seeking the adoption records of Judge Roberts's children. No one has come forward with any suspicions that there are any improprieties in the paperwork, and this would seem to be a fishing expedition.
The way this is playing out, I don't think Bork is the correct example for this strategy. Better would be that the media is trying to Baird Judge Roberts. Most of you should recall Zoe Baird, the Clinton nominee for Attorney General that had been undone by having employeed illegal aliens in her home. It is surprising that Democrats, who between Baird and Clinton said that private is private and has no impact on a person's public works, would seek out this type of information. A commenter on another blog pointed out that it is entirely appropriate for liberals to dig into Judge Roberts's past in order to prevent someone getting on the Supreme Court who might attack the right to privacy. (The commenter had expressed it, I hope, ironically.)
Then again, if there is something that comes up, then Republican precedent would set it that they would have to withdraw the nomination. Of course, it would be interesting to watch the contortions performed to justify Roberts. If Washington shows us anything, it is that history is no basis to form future opinion.