Among many high White House officials, Attorney General William French Smith is viewed as a political lightweight who repeatedly has embarrassed his chief client, the president of the United States.

But these same officials say in almost the same breath that Smith isn't going anywhere.

The client likes his attorney general, who is also his longtime tax attorney and his friend. And President Reagan, they say, also has made it clear in private conversations that he intends to stick by his embattled chief law enforcement officer.

"Smith is an embarrassment," one well-placed official said. "He is in over his head and he has many blind spots. But the president likes him, and that's what matters."

The attorney general's present difficulties have resurrected discussion of what some administration officials call "the Smith problem." These difficulties result from Smith's claim of tax deductions for an investment tax shelter of the kind frequently disallowed by the Internal Revenue Service in the past, and from a $50,000 severance fee he received from a steel company owned by a Reagan friend nine days before Smith became attorney general.

"What does this tell you?" an administration official asked rhetorically yesterday. "Our most persistent problem in the polls is that Reagan is seen as a rich man's president. Here you have the attorney general, one of his closest friends, taking two and a half times more tax deductions than the average working man earns in a year and playing right into that perception."

No White House officials will criticize Smith for the record. They emphasized that the official administration view of him was uncritical and supportive. They are aware that Reagan has made it clear that he wants no staff sniping at Cabinet officers in general and that Smith, in particular, enjoys a personal relationship with the president unequaled by other Cabinet officers.

When articles have appeared indicating that Smith would leave the Cabinet and be replaced by White House counselor Edwin Meese III or chief of staff James A. Baker III, they have promptly been denied by the administration. Smith is known to be sensitive about such stories, and administration officials are careful about provoking his resentment.

Yesterday, after it became known at the White House that The Washington Post was publishing an article containing criticism of Smith by administration officials, Baker issued this comment:

"The president knows that Bill Smith is a man of honor and integrity. There is in no way a feeling at the White House that he is a political liability. The president retains confidence in him."

Despite such declarations, dissatisfaction with Smith runs deep within the administration. It has bubbled up periodically since early last November, when Smith staged an end run on the White House staff and arranged his own meeting with the president to discuss the pending voting rights bill.

The result of Smith's conversation with Reagan was presidential support for two weakening amendments to legislation favored by a large bipartisan majority in both houses of Congress. The presidential position disturbed some high White House aides, who accurately predicted that it would make Reagan appear as if he were dragging his feet on extension of the act.

It took the Reagan administration six months to extricate itself from this compromising political position. The president finally did this earlier this month with support of an extension that preserves all the essential features of the liberal version of the bill Smith had opposed.

After that episode, some administration officials complained that Smith, despite presenting the appearance of really being a team player, really wasn't, in many circumstances.

One aide called him "a pleasant country lawyer who is over his head at Justice." Another said that Smith was presenting his own agenda as Reagan's to the detriment of the president.

Smith's acceptance of the severance fee, a practice that is contradictory to past Justice Department opinions on the subject, has caused particular concern at the White House.

There are darker suspicions within the administration over Secretary of Labor Raymond J. Donovan, who has long been under investigation, most recently over allegations that he and his New Jersey construction firm have ties to organized crime.

None of the administration officials express misgivings that Smith has done anything illegal, and several volunteered the view that they were certain that he had been careful to stay within the law.

One added sarcastically, however: "It would help if we could say something a little more constructive about the head of the Justice Department."

The criticisms of Smith include large and small items and come from varying constituencies. He has been rapped for being insufficiently attentive to staffing the Justice Department with minority members, especially blacks, and also for failing to pay much attention to the job claims of Reagan conservatives.

This seeming contradiction may be explained partly by Smith's background as a smooth-talking establishment tax lawyer for a wealthy set that was not noted for sensitivity to affirmative action claims or the issues that motivate the New Right.

Smith was traveling in California, where his current problems did not come up during a brief question-and-answer session with reporters who were mostly concerned about U.S. immigration issues.

Late in the day, his press spokesman, Thomas P. DeCair, said, "Our experiences with comments from anonymous officials show that they almost always lack full knowledge of the facts. There is a natural and proper tension between the White House and the Justice Department . . . . The attorney general is carrying out the objectives of the president."