Supporters and detractors agree: He’s not your off-the-rack president. He doesn’t conform to expectations. He doesn’t do things the way his predecessors did. He may not be exceptional – let’s postpone for the moment a discussion of how he’ll rank in history – but George W. Bush may be the presidential exception that proves the rule.

Until last week, no one ever thought of this rule, but among modern presidents, Mr. Bush may be the first to break it: Chief executives don’t undertake major initiatives in the final quarter of their tenure.

But Mr. Bush’s speech Wednesday night outlining a new surge in Iraq – raising the stakes in the Gulf region rather than lessening the American commitment there, after a disappointing performance and disheartening public support – broke new ground in the annals of the presidency, at least for the last three-quarters of a century. Then again, the only rule that explains Mr. Bush is that he does not live by other presidents’ rules.

Other presidents have done little in the final quarter, allowing of course for the wrinkle that single-term presidents don’t know that their fourth year is the final quarter. But the last four two-term presidents (and for argument’s sake I am including Franklin D. Roosevelt, who didn’t know he’d be going into overtime with third and fourth terms) have spent their final quarters responding to events rather than initiating them.

Not so Mr. Bush. He’s responding, of course, to the deteriorating condition in Iraq. But he is initiating a new offensive there, an offensive that will have its first front on Capitol Hill, where newly emboldened congressional Democrats already are scheming to thwart him. This new offensive – first in Washington, then in Iraq – is in keeping with his offense-minded presidency, which is peculiarly well-suited to the sports metaphors that we columnists try so hard to avoid.

Mr. Bush has broken rules before. As a minority president who won his election in the Supreme Court, Mr. Bush might have been expected to tread lightly, seeking conciliation rather than confrontation with the Democrats who believed the election had been stolen from them. But he did not accede to the Jeffersonian notion that big changes should not be forced by small majorities. He moved ahead with tax cuts, new initiatives that challenged traditional distinctions between church and state, and a muscular foreign policy that eschewed the diplomatic niceties and pro-forma consultations that guided established diplomatic practice as much in the Clinton years as in the Nixon era.

“Any initiative he takes despite the lessons of history is altogether in keeping with his character throughout his presidency,” says William E. Leuchtenburg, an emeritus presidential historian at the University of North Carolina. “He is a man who is not at all guided by the knowledge of the past.”

That can be limiting – or liberating.

Now Mr. Bush is pressing ahead in Iraq, dangerous territory in a literal sense, dangerous territory in a metaphorical sense. Dwight Eisenhower was on the defensive in his final two years, making few if any initiatives. Ronald Reagan was preoccupied with the Iran-Contra affair, a presidential defensive posture with few analogues. Bill Clinton’s final quarter began with his impeachment trial, an ordeal that gave new 20th-century meaning to the notion of the president as defendant.

Big initiatives, including doomed ones, often come in the first and fifth years of a presidency, mostly because there is nothing like a victory in a national election to fortify a president and to free him to spend his political capital. That’s why Bill Clinton pushed ahead with an aggressive economic program (which barely passed) and an even more aggressive health-care overhaul (which bombed) in his first year, and why Ronald Reagan pressed ahead with his tax and budget cuts (which passed) in his first year and his tax overhaul (which many Democrats embraced on the way to victory) in his fifth year. The biggest presidential miscalculation of modern times may have been Franklin Roosevelt’s court-packing plan, which he unveiled, to the distress even of some Democrats, in his fifth year.

And yet, major initiatives in the last quarter of a presidency are not entirely unknown, though their results can offer little comfort to the president.

Woodrow Wilson sought Senate confirmation of the Versailles Treaty, with its League of Nations clause, and not only was he defeated in a bitter battle, but also he suffered a debilitating stroke that ended his presidency; he rode to the Capitol for the inauguration of Warren G. Harding but did not stay for the proceedings.

Nearly a century earlier, in his last year in office, Andrew Jackson issued the Specie Circular that long has been the curse of befuddled high school history students but in the short term was the curse of Martin Van Buren, who was forced to deal with the Panic of 1837 that the action precipitated.

Now Mr. Bush is capping his crowded hour on the world stage with a crowded coda.

The president does things his way and sees things his way. His opponents deride him for this, though very likely they would applaud him for his courage and vision if his views were more congenial to theirs and if he were pressing ahead bravely on behalf of initiatives they supported. The line between presidential fearlessness and presidential folly is sometimes a partisan one, bringing to mind the old Tip O’Neill dictum that where you stand depends mostly on where you sit.

Mr. Bush sits in the Oval Office in the first presidency of the 21st century and in the first presidency of the terrorism era. It is his view that the terrorist attack of 2001 changed all the rules of national security. Now he’s breaking an unspoken, heretofore unrecognized, rule of the presidency.

Rules are made to be broken, but sometimes rules break presidencies. That’s why the president’s Iraq policy has the potential to change the rules, or merely to reinforce them for a new century.