At least the fringe (read "controlling portion of the") Republicans are not shy about opposing anything Obama. Rush Limbaugh has gone on record already as referring to Obama AND his nominee Judge Sotomayor as "reverse racists."
Part of the "basis" for this assertion is the following sentence said by Judge Sotomayor: "I would hope that a wise Latina woman with the richness of her experiences would more often than not reach a better conclusion than a white male who hasn't lived that life." The problem with using this as the launchpad is that this is one sentence in a speech, buried in the middle and completely out of context. If you read the entire speech (available here), you see that the overall message of the speech is precisely the opposite of what the Limbaugh Republicans would have you believe. In fact, she maintains that while she is aware of her limitations (a message Rush would be better served by hearing), she hopes that she will use her experiences and life story judiciously: "Hence, one must accept the proposition that a difference there will be by the presence of women and people of color on the bench. Personal experiences affect the facts that judges choose to see. My hope is that I will take the good from my experiences and extrapolate them further into areas with which I am unfamiliar. I simply do not know exactly what that difference will be in my judging. But I accept there will be some based on my gender and my Latina heritage." Finally: "I can and do aspire to be greater than the sum total of my experiences but I accept my limitations. I willingly accept that we who judge must not deny the differences resulting from experience and heritage but attempt, as the Supreme Court suggests, continuously to judge when those opinions, sympathies and prejudices are appropriate."
Another question involves her apparent position on the New Haven affirmative action case. In this case, a white firefighter sued after the results of a promotion examination produced an overwhelming majority of caucasian promotions. The city rejected these results in order to comply with the Civil Rights Act, yet to comply with this law rendered the city vulnerable to this lawsuit, which of course, is now a Right rallying cry as well "Affirmative Action judge!" Never mind that she wrote no opinion on this case, and the rejection was en banc.
Rather than take a couple Republican Talk Show cherry picked examples, it's probably more prudent to look at a compilation of Judge Sotomayor's time on the bench, which you can find at SCOTUS blog.
There could be legitimate reasons to oppose the appointment of Judge Sotomayor to the bench, but nothing that's been run up the flagpole yet by the talking heads on the right. Perhaps that's not such a bad thing.