To his critics, to those who suggest that he is not sufficiently experienced or qualified to take over the presidency, Dan Quayle has one message: "I'm more determined than ever to succeed.

"I will prove my critics wrong," he said Friday in an interview aboard Air Force II as he returned to Washington from a trip to Detroit. "When that will be, only time will tell."Quayle gives no outward sign of being perturbed or personally wounded by the avalanche of stories and speculation that re-emerged last week questioning his fitness to succeed the president, to say nothing of the late-night television jokes, such as Johnny Carson's suggestion that Quayle was reading the Cliffs Notes version of the Constitution.

But an edgy tone creeps into his voice when he's asked what he would like to say to those who claim he's in over his head.

"Judge me on my public career," he replies. "I can't ask for anything more and I've gotten a lot less. Look at what I've done as vice president; look at what I did for 12 years in Congress; judge me on what I've accomplished."

For Quayle, last week may have been the most trying time since those weeks immediately after his selection as the Republican vice presidential nominee in August 1988. President Bush's heart flutter immediately focused the nation's attention on the man who potentially would succeed him, and in many Americans this stirred deep anxiety.

A USA Today poll published last week, for example, showed that 43 percent of those surveyed felt he was qualified to become president, but 46 percent did not.

A poll by Time magazine and the Cable News Network Saturday revealed most Americans harbor deep doubts about Quayle.

The survey of 500 Americans conducted late last week showed only 34 percent of Americans think Bush should keep Quayle as his running mate.

Nearly one in four of those surveyed said keeping Quayle on the ticket would make them less likely to vote for Bush in 1992 and 52 percent favor dumping the vice president.

In many ways, Quayle is a man caught in the middle, a victim to some extent of his own position and the way he has carried it out to the satisfaction of George Bush.

Like most vice presidents, he has worked behind the scenes, raising money, maintaining ties with state and local officials and taking on such non-glamorous duties as heading the Space Council and the Competitiveness Council.

The bottom line of all this: no news. So reporters' interest has dropped off - Quayle frequently makes official trips without any accompanying reporters - and the public remains locked into the '88 image of a good-natured buffoon.

And, experts say, unless he gets a chance to serve as president and performs well, this may never change.

"The sad fact is he's been a pretty competent vice president, yet it's had no bearing on the public image set in concrete in '88," says Thomas Mann, director of governmental studies at the Brookings Institution, a middle-of-the-road Washington policy center.

"Quayle and his aides must be enormously frustrated. A lot of people made the judgment (in '88) that he's not presidential timber, and unless he gets a chance to serve as president, that won't change."

Quayle himself sidesteps questions about taking over the presidency, implying that they are unseemly.

"I know what the job is," he says in one of his rare comments. "I work for the president every day."

On Friday's trip to Detroit, Quayle did what he does best: interacting with people in one-on-one, informal situations. He acknowledges that he does not perform nearly as well on television. Part of this, he says, may have to do with the fact his eyes are extremely sensitive to bright lights. But there also is a lingering sense that he is so intent on avoiding mistakes that he comes off as too controlled and almost hesitant.

But in Michigan, on his own, Quayle was mischievously spontaneous when he made an impromptu stop at a highway diner near the airport and spotted a young man on a pay telephone. Quayle took the phone from him, spoke to the woman on the other end and then turned to the man and said, "You've got a date for tonight."

Later, he said with a chortle: "I'm a matchmaker. He was calling his girlfriend, and I said, `Do you want me to get you fixed up for tonight?' and so I got on the phone and said, `Are you available?' "

As Quayle and his entourage moved through the diner, the young man could be heard on the phone trying to convince the woman that she actually had spoken with the vice president. "I swear to God," he kept saying. "I swear to God."

Later, in a visit to an eighth-grade science class at

Faith Christian Academy, Quayle listened intently as 14-year-old Ozell Wells described all the things he thought should be done to improve the space shuttle.

"Do you have any free time?" he finally asked the obviously well-informed Wells. "I'd like to make you an honorary adviser to the Space Council."

At the Detroit Center Tool factory, Quayle met with business leaders and representatives of the Big Three automakers in anticipation of a coming trip to Japan and Indonesia that will center on trade. This is typical, necessary vice presidential duty, he said.

Asked during a news conference at the factory how he is dealing with the bad publicity, he guardedly replies: "I do the job, just like today. I'm here helping the president."

But his more candid view of the media assault of the last week slipped out at the school. As a young girl with pigtails wrote down his every word, Quayle noted that she was a reporter for the school paper.

"We'll see how you report it (his appearance there) and how they report it," Quayle said, gesturing at the journalists assembled at the rear of the room. "And I bet yours is more accurate."