Yes, consent, nowhere does it say that the legislators get to have a say in the procedure other than to give advice or, possibly, withhold their consent. Of course, the founding fathers assumed they would ask questions and not just knee jerk withhold consent without any firm reason other than "feelings".
No reason for withholding consent was mentioned either IIRC. It is not rational to assume they would give uninformed consent or consent against their better judgement. But this is beside the point. If they didn't think Ginsberg should have been confirmed they should not have voted for her. They use as the excuse "Clinton" deserved to have whoever he wanted confirmed. I take strong issue with that and would vote to keep anyone who thought that way out of the US Senate. They are unworthy. To use the same logic to say Miers should be confirmed ONLY because Bush wants her to be is equally insulting.