Vice President Cheney, on a stop here Saturday, continued his role as the campaign's point man for delivering ever-sharper attacks on John F. Kerry, asserting that if the Massachusetts senator had been president in recent history, the Soviet Union might not have fallen, a nuclear-armed Saddam Hussein could be in control of the Persian Gulf and the United States might have ceded its national defense to the United Nations.

Cheney said he was inspired to conjure the world Kerry would have presided over by the Democrat's assertion that he could have done a better job as president.

"Yesterday and again today, John Kerry's running around campaigning, claiming that the world would be a whole lot better if he had been president," Cheney said to boos. "That is an interesting proposition. Maybe we should consider it."

Citing Kerry's opposition to some Cold War weapons systems and to the 1991 Persian Gulf War, and statements the senator made in the 1970s calling for U.N. approval before deploying U.S. forces, Cheney belittled Kerry as a leader who would have made the country vulnerable and undermined world progress.

"One way the world might look if he had been in charge is, he would have ceded our right to defend ourselves to the United Nations. . . . If John Kerry had been in charge, maybe the Soviet Union would still be in business. . . . If John Kerry had been in charge, Saddam might well control the Persian Gulf today. . . . He might well have nuclear weapons," Cheney said. "It's a good thing he wasn't in charge."

Later in Colorado, Cheney added another item to his list of Kerry "what ifs," saying: "If the position he's taken over the years really mattered . . . our military would be without many of the weapons we use today in the war on terror."

Cheney did not mention that he had opposed some of the same weapons systems, or that Kerry has rejected his earlier U.N. comments, made in the aftermath of the Vietnam War.

"That's ludicrous," said Sen. John Edwards (N.C.), Kerry's running mate. "They want to talk about bizarre fantasy worlds because they can't talk about their record of failure. We don't have to create a fictional universe in order to understand what their incompetence has meant for this country. It's all too real."

Vice President Cheney campaigns with GOP Senate candidate Pete Coors in Grand Junction, Colo.