Speculation swirled yesterday about the vice presidential picks of both White House contenders, as Senator Obama’s campaign announced the Illinois senator would hold a major event Saturday in his home state, at the site where he announced his candidacy last year. The Associated Press reported that Mr. Obama’s handpicked running mate would be at his side during the rally, which could be the first time the two campaign together. Mr. Obama is expected to announce the selection in e-mail and text message to supporters any day now. The speculation centered on three men: Senator Biden of Delaware, Senator Bayh of Indiana, and Governor Kaine of Virginia. The selection of Senator Clinton would now be considered an enormous surprise, although it has not been ruled out. Mr. Obama and his running mate will tour key battleground states leading into the Democratic National Convention next week in Denver. Meanwhile, the National Review and Politico reported that Senator McCain is seriously considering a running mate who supports abortion rights, such as Senator Lieberman of Connecticut or Governor Ridge of Pennsylvania. His aides are reportedly reaching out to donors and Republicans activists to prepare them for the possibility, which would roil a party overwhelmingly opposed to abortion. His selection is expected on or around August 29, the day after the Democratic convention concludes.