Sen Lamar Alexander, R-TN, chairman of the Senate GOP conference, announced his opposition to Elena Kagan Friday, rounding out the full Republican leadership rejection of President Obama's Supreme Court pick.

Senate Majority Leader Harry Reid, D-Nev, has set aside the first week of August, before members leave town for a month-long recess, for debate and a vote on Kagan.

It is not yet known if a GOP senator will choose to filibuster the high court nominee, though Kagan is expected to win confirmation in the end.

So far, Kagan has only two GOP supporters, Sen Lindsey Graham of South Carolina and Dick Lugar of Indiana.