Last week Democratic senator Ben Nelson announced that he will vote against the Kagan nomination. By my count, 31 Republican senators have also stated that they will vote against Kagan.
So far as I’m aware, five Republican senators—Bond, Brown, Brownback, Cochran, and Enzi—have not yet said how they will vote. Brownback, Cochran, and Enzi voted against the Sotomayor nomination, so it is reasonable to expect that they will vote against Kagan. (No senator who voted against Sotomayor has yet declared for Kagan. Three senators who voted for Sotomayor—Alexander, Nelson, and Voinovich—have declared against Kagan.) Bond voted for Sotomayor, and Brown was not then in the Senate.
There are three other Democrats who are viewed as possible negative votes: Conrad (North Dakota), Lincoln (Arkansas), and Webb (Virginia).
So a conservative guess is that there will be at least 35 votes against Kagan.