WASHINGTON - Sen. Barack Obama began trying to rally the Democratic Party around him on Thursday. He struck a tougher tone against Sen. John McCain, saying McCain is "losing his bearings" in his pursuit of the presidency.

Even as Sen. Hillary Rodham Clinton persisted with her campaign for the Democratic presidential nomination, Obama made a celebratory return to the Capitol, where he received an enthusiastic reception on the floor of the House in an appearance staged to position him as the party's inevitable nominee.

Addressing concern among some Democrats that Clinton would fight on to the national convention in late August, Terry McAuliffe, chairman of the Clinton campaign, suggested that the race would end quickly after the final primaries in early June, sparing the party a potentially debilitating summer-long battle.

"After June 3, this is going to come to a conclusion," McAuliffe said on NBC's "Today" program.

Other close Clinton allies said much the same thing, evidence of a growing consensus that Clinton has another four weeks to make her case to voters and superdelegates but then should exit quickly if she has not somehow turned the race around.

Obama made no public effort to pressure Clinton from the race, and in interviews with CNN and NBC News he praised her as a formidable candidate who could not yet be counted out. But he said that he was likely to lock up a majority of the pledged delegates -- those awarded by voting in the primary and caucus states -- after the Kentucky and Oregon primaries on May 20, and that at that point he could declare victory.

While he was respectful to Clinton, Obama seemed eager to challenge McCain. Asked on CNN about McCain's recent statement that the radical Palestinian party Hamas, considered by the United States to be a terrorist organization, would favor Obama's election, Obama said it was offensive and called it a smear.

"And so for him to toss out comments like that I think is an example of him losing his bearings as he pursues this nomination," Obama said.