They insist that the confirmation process be careful and deliberate. They claim that they want a thorough investigation of her qualifications to ensure that she is an appropriate and suitable person to serve as a Justice, but that's not the real reason for the slowdown.
The real reason for the slowdown is to keep Sotomayer from voting on which cases will be heard in the upcoming Supreme Court term.
The U. S. Supreme Court begins it's annual session on the first Monday in October. The term runs through the end of June.However, some of the Justices' most important work of the year actually takes place in August and September, before the term begins.
That's when the Justices meet to decide which cases are going to be heard in the upcoming term and which cases will be rejected. Four Justices must vote in favor of hearing a case, or the case doesn't get heard by them at all. About 5,000 cases per year get appealed to the Supremes, but only about 75 cases are accepted for review.
By stalling on her confirmation, Republicans can keep Sotomayor from voting on which cases to hear in the upcoming term. That's important, because it keeps Sotomayor from being the deciding vote on getting certain injustices actually reviewed by the Supremes. As a result, many cases, in which Republicans want to preserve injustice, will fall short of that necessary fourth vote to get heard, thus preserving the injustice.
It's just another Republican Party dirty trick. More government by scam.