Top supporters of Senator Barack Obama, joined by at least one prominent but uncommitted Democrat, raised the pressure Sunday on Senator Hillary Clinton to bow out of the presidential nominating race if she fails to score clear victories in two big-state primary contests Tuesday.

"I just think that D-Day is Tuesday," said Governor Bill Richardson of New Mexico, a former Democratic presidential hopeful who has yet to throw his weight behind either leading candidate. He said the increasingly negative campaign advertisements aired by both Democrats made it more urgent that the party unite quickly behind a nominee.

Texas, Ohio, Rhode Island and Vermont hold primary contests on Tuesday, and the Clinton campaign, trailing in the delegates needed for nomination and having lost 11 straight contests, has said the New York senator needs to win either Texas or Ohio. Both candidates were campaigning Sunday in Ohio.

With Senator John McCain, the presumptive Republican nominee, able to profit from the Democrats' internecine battles, the chairman of the Democratic National Committee, Howard Dean, leveled unusually tough attacks against McCain on Sunday.

"He runs on his integrity, but he doesn't seem to have any," Dean said on CNN. "John McCain has a history of doing what it takes, regardless of what the ethics are. I think he's going to be a flawed candidate." He appeared to be referring to reports, including one in The New York Times, that suggested that McCain sometimes applied tougher ethical standards to others than to himself - a charge McCain has spiritedly denied.

Richardson, saying that it was vital to Democrats' hopes in the November election to mount a positive, unifying campaign, said on CNN that "whoever has the most delegates after Tuesday, a clear lead, should be, in my judgment, the nominee." For that to be Clinton, she would have to dramatically exceed the results predicted by polls, which now show Texas a virtual toss-up after weeks of steady progress there by Obama, while Ohio voters narrowly favor Clinton.

In the smaller states, Clinton holds a lead in Rhode Island polling while Obama has the edge in Vermont.

Howard Wolfson, the Clinton communications director, offered no hint Sunday that the senator was close to withdrawing. He argued again that Clinton had shown her ability to win populous states like California and New York that will be needed for victory in November. Clinton, he said, had "a very strong case to make" that she would be the stronger Democrat against McCain.

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