Senator Jeff Sessions is going to "try" to give Sonia Sotomayor a fair hearing in her confirmation process. Well, that's big of him. That's your job, Senator. To give the president's nominees a fair hearing. To screen them, meet with them, ask them questions, hear their answers, all BEFORE you decide to reject the nominee. You wouldn't want to pre-judge the issue based on your own political biases (you know, that she's the nominee of a Democratic president while you're a Republican) instead of waiting to hear all the evidence and judge the case on its merits.
I have a sneaking suspicion, though, that Sen. Sessions (and probably a few others) aren't all that interested in hearing the real evidence of Judge Sotomayor's record. They just want to assert as loudly as possible that she is just another lawless, irresponsible, activist liberal judge who doesn't follow the Constitution, but follows her heart to come up with whatever result feels right to her in any given case. If they succeed in saying it enough, the evidence of her actual judicial record be damned, then they can automatically discredit any ruling of hers they might disagree with someday.