Yes, they do have that "right" (it is just a custom).
The plan would be to have the Dems fillibuster Estrada and then refuse to blue slip Janice Brown, and then present a case that the Democrats are racists. Seems a bit tenuous in Brown's case, as people like Sharpton would just call her an "Uncle Tom", and most blacks would buy it, as they did with Clarence Thomas. However Latinos are far more open, and will be mad.
Senate Judiciary Chairman Orrin Hatch says he plans to change the "blue slip" tradition, referring to blue-colored approval papers that senators are asked to submit on nominees to fill vacant federal judgeships in their state. For the past few years, both home-state senators had to submit a positive blue slip for a nominee to be even considered by the Judiciary Committee. Under Hatch's plan, a single negative blue slip from a senator won't be enough to stop a Bush nominee. "I'll give great weight to negative blue slips, but you can't have one senator holding up, for instance, circuit nominees," said Hatch, R-Utah.