The answer at this point is — nobody knows, or could possibly know.
Solicitor General Kagan has almost no paper record of scholarship on Indian law, no judicial opinions, and little else in the way of a paper trail. Her most intimate association with Indian Country is her membership (now likely former) on the board of the American Indian Empowerment Fund (as noted here), which probably came about as a concomitant duty related to her Harvard deanship and duties in filling the Oneida Chair at Harvard Law. As is well known, Harvard Law has had some difficulty in completing the requirements of the Oneida endowment (hiring a full-time Indian law prof), as the Chair is always filled by visitors. What this means is anyone’s guess, though some of my former law school colleagues are certain it is a bad thing she had trouble hiring minority law profs.
The only known impact of Kagan’s nomination if she is confirmed, is that she will likely be forced to recuse herself in the 2010 Term’s lone (so far) Indian law case, United States v. Tohono O’odham Nation (No. 09-846). Who knows how that will affect the decision, though the T.O.N. would only have to find four Justices to prevail (as would happen in a 4-4 tie). Once the T.O.N. case is decided, we may hear much more from a Justice Kagan, who perhaps will be tapped write some of the Indian law decisions (as junior Justices often are).
Which leads to my final comment. A Justice Kagan is yet another player from the elite of the legal profession, an elite that rarely has even more than a passing interest in Indian law and Indian Country. From Justice Brennan referring to Indian law cases as “chickenshit” (page 435 of The Brethren), to the modern and open hostility of most Justices to Indian cases, this does not bode well. It could, if a Justice Kagan is open-minded and willing to listen and learn, but more likely than not, she (as do most or all of the other Justices) may find her Indian law assignments a burden. That would be a shame.
Perhaps we’ll see.