From the SCOTUS blog Lawhawk linked to:

Opponents’ first claim – likely stated obliquely and only on background – will be that Judge Sotomayor is not smart enough for the job. This is a critical ground for the White House to capture. The public expects Supreme Court Justices to be brilliant. Harriet Miers was painted (frequently, by conservatives) as not up to the job. The same claim (absurd to anyone who has talked with him) is still made by the left about Clarence Thomas. By contrast, John Roberts was described as brilliant and Sam Alito as exceptionally smart.

The objective evidence is that Sotomayor is in fact extremely intelligent. Graduating at the top of the class at Princeton is a signal accomplishment. Her opinions are thorough, well-reasoned, and clearly written. Nothing suggests she isn’t the match of the other Justices.