When President Reagan was in the hospital recovering from cancer surgery, his chief of staff and self-styled "prime minister" wanted to make the daily round trip from the White House to Bethesda Naval Hospital by helicopter. Donald T. Regan dropped the idea after First Lady Nancy Reagan expressed doubts about it, but Regan's flight of fancy expressed a symbolic truth about his self-importance.

As the president heads into the rough waters of his second term, Regan is big stuff in the White House. He has been indisputably in charge since taking over from James A. Baker III last February and virtually a deputy president since Reagan's surgery.

Departing from tradition, Regan saw to it that he was introduced at presidential speeches. He organized the White House in a hierarchal fashion that he preferred to describe as corporate, becoming the funnel to the president for other aides who might have brought unpleasant information. Only Vice President Bush and national security affairs adviser Robert C. McFarlane have independent access, and Regan's men have denigrated Bush and made no secret of their displeasure with McFarlane.

By his own account, Regan does not desire to change the president's thinking. Instead, he has urged Reagan not to demonstrate "weakness" by compromising with his critics.

Numerous Republican officeholders think that Regan has become too big for his britches. Even some of Regan's aides suggested to him that he was overdoing the prime minister routine, and Regan made a point of staying off of the speaker's platform when the president resumed his tax-overhaul campaign.

In the current issue of Business Week magazine, Regan offers revealing glimpes of his thinking. "One of the reasons I've gained so much prominence is because of the blame coming my way," he said. "It's kind of nice for the president to be able to lay off the blame and say, 'I didn't do it; it was somebody down the line.' There's nothing wrong with that as long as it goes both ways. Remember when things go right that Regan had something to do with it, however little."

Baker would never have put down the president with this faint praise of himself. Nor would have William P. Clark or Edwin Meese III when they were Gov. Reagan's chief aides in California.

Taking their cue from their boss, Regan's aides seem more loyal to him than to the president as they march in lockstep, using identical phrases in defending every action of the chief of staff. Recently, one subordinate credited Regan for resolving the TWA hostage crisis and for congressional approval of 50 MX missiles. In fact, McFarlane was point man on the hostage crisis, where the president demonstrated skill and restraint, and was architect of the MX compromise, if anyone wants to call such a limited victory an achievement.

The real question in the White House should be not who is responsible for Reagan's victories but who is willing to warn him of probable defeats that lie ahead. On this score, Regan has been tried and found wanting. He refuses to take seriously the well-founded assertion of Senate Republican leaders that the administration is fleeing from its responsibility to address the budget deficit. He does not see it as his role to open the president to a variety of options, even though Reagan tends to shine when offered choices that go beyond ratification of his prejudices.

Neither ego nor ideology is Regan's biggest problem, however. He has been hurt most by political inexperience and failure to recognize that politics is a special art about which he knows very little. It is doubtful that Regan, at Merrill Lynch, would have employed a politician who didn't know a stock option from his elbow. But his contempt for politicians and what they have to teach him is ill-concealed.

Regan has much to recommend him personally. What he lacks in political understanding, he makes up for in directness and candor. He has had the courage to attach his name to his opinions, suffering less than others from the Washington mania for speaking on "background." It is certainly no mystery why Reagan likes someone who shares his outlook, optimism, competitiveness and robust good humor to the degree that Regan does.

But at a time when the president desperately needs to set aside some cherished fallacies -- that the deficit will disappear through growth, for example, or that the South African government is "reformist" -- his chief of staff does not seem up to the task.