When President Bush and Vice President Cheney sit down together on Thursday for their long-anticipated meeting with the 9/11 commission, it will cap a week that has, like no other in Mr. Bush's presidency, been dominated by the White House's No. 2 man.

It was Mr. Cheney who used such red-meat language against Democratic presidential contender John Kerry in a speech Monday that the president of the host college publicly objected to "the content and tone" of the vice president's remarks and offered Senator Kerry a similar speaking engagement.

It is Cheney who is at the center of a long-anticipated Supreme Court case, argued Tuesday, over his energy task force - and the breadth of the zone of privacy in which the executive branch of government may operate. Cheney has long advocated restoration of the White House's powers to pre-Watergate levels.

But it is Cheney's joint appearance with the president Thursday that has reignited most fully the question of exactly how powerful a No. 2 he is. Political observers agree he is, hands down, the most powerful vice president in history, with crucial input in the central issues of the day, including the war on terror and in Iraq.

Democrats have seized on the White House's requirement that the two men talk to the 9/11 commission jointly (rather than separately) as evidence that Cheney is Bush's ventriloquist, and that after three-plus years on the job, Bush is still not up to the task. The issue of Cheney's role - shadow president or just a helpmate with unprecedented influence? - has reached almost metaphysical levels of speculation.

Cal Jillson, a political scientist at Southern Methodist University in Dallas, who knows Cheney from his days on SMU's board of trustees, sees two spheres of opinion on the vice president - the "elite" Washington view and general public opinion. While pundits and the press focus on the wider tableau of the Washington power structure, including Cheney's role, the public is more focused solely on Bush.

The new bestseller on the Bush White House's runup to war with Iraq, "Plan of Attack," by investigative reporter Bob Woodward, characterizes Bush as clearly in charge - no doubt a key reason the Bush campaign website recommends the book. But for those watching events daily, no one account is likely to sway everyone.

"What the Woodward book did was to get rid of the cartoon imagery of how the two of them interact, the idea of the little diminutive Bush sitting on Cheney's knee or being unable to talk while Cheney drinks water," says Professor Jillson. "That caricature is still in the elite mind-set, not so much in the public mind-set. It probably never was in the public mind quite the way it was for the people who follow this thing day to day."

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