I'm not and probably never will be a politician, and my instincts on this are probably all wrong, but while knowledgable folk like Kevin look for lines of constitutional inquiry that might have been more effective for the Democrats, I can't help wondering why no one pressed him on his insistence that he had an obligation not to answer meaningful questions. At times he refused to answer on the basis that he couldn't do so without a specific case to evaluate through the judicial process. At times he refused to answer because answering might commit him to judging in a specific way in cases likely to come before the Court.
There are a couple problems with these answers.
First, they're not consistent. If every case is distinct and can only be judged after considering the particulars, expressing opinions on general constitutional principles cannot prejudge any particular case. Until justices go through the judicial process, they presumably don't know which constitutional principles apply and to what extent. Without reference to a particular case, expressing opinions on Constitutional principles is not prejudging and does not commit the judge.
Second, as many have noted, justices express opinions all the time. It's their job. Scalia, Thomas, Sutter, et al have expressed opinions on issues likely to come before the Court many times, and will continue to do so. Alito has done so as an appelate judge. Members of the Court have expressed opinions in speeches, books, and articles. Before he was a judge, Alito expressed opinions as a government lawyer. Yet somehow, we're all supposed to accept that expressing opinions in response to the questions of the judiciary committee would compromise his judicial objectivity. I would like to have heard Alito explain why expressing opinions in public, before the people he will spend the rest of his life judging, prior to becoming a judge, was different.
It's a line of questioning that might not have been easy to deflect. He might, for example, have had a hard time asserting that he can't answer questions and asserting that he can't explain why. I would have enjoyed listening to him explain why only the public has no right to know, or trying to claim that he does not, in fact, have opinions on controversial matters of great public import. I would have enjoyed hearing him explain how the judicial process insulates his future judgements on the Supreme Court from the opinions he's expressed before, but not from opinions he expresses before a Senate committee. I would have enjoyed hearing him explain how keeping the public ignorant of a judge's deeply held views is equivalent to a judge not having deeply held views.
It might not have changed the outcome, but it would have been more edifying than what we had.