EXETER, N.H. -- Rep. Jack Kemp (R-N.Y.), a former professional football quarterback, doesn't particularly like the use of sports metaphors to describe his campaign for the Republican presidential nomination. But he will go along with the device, as he did here Friday when asked about his late-moving drive to overtake Vice President Bush and Senate Minority Leader Robert J. Dole (R-Kan.).

"It's probably the third quarter or just entering the fourth quarter," he said. "Bush and Dole are playing not to lose. I'm behind, but playing to win."

Warming to the subject, Kemp then compared himself with the Green Bay Packers' Bart Starr, the dominant quarterback of the 1960s.

"They are scared of their shadows and their records," he said of his front-running rivals, "and I'm a Bart Starr who is willing to throw on third and one."

Not long ago, it was third down and one yard to go for Kemp, who could not seem to move out of single digits in polls here, in Iowa and elsewhere. But like Starr, the quarterback who was known to gamble with a long pass in just such a situation, Kemp went on the offensive.

In television commercials and personal appearances across New Hampshire, Kemp is portraying Bush and Dole as eager to raise taxes, increase oil and home-heating fuel prices and freeze or cut Social Security benefits.

In one commercial, Dole is attacked for suggesting that he could support an oil import fee, while Bush is shown meeting with King Fahd of Saudi Arabia and accused of trying "to get the Saudis to prop up oil prices."

The Kemp Social Security commercial, which went on the air last week, attacks both GOP front-runners for supporting a 1985 Senate Republican budget resolution that would have frozen cost-of-living adjustments in several federal programs, including Social Security. Kemp claims credit for persuading President Reagan to scuttle the measure.

Kemp is pressing the attack and these themes on the stump, portraying Bush and Dole as "old guard Republicans" and, invoking a time-worn Democratic technique, identifying them with "the {Herbert} Hoover wing of the party." With his rapid speaking style, the excitable Kemp sometimes lumps his rivals into a single political behemoth, as in, "I think I'm the alternative to Bushdole."

The attacks have worked, to a point. And they also appear to have drawn blood. While Dole has gone around New Hampshire attacking the ads, Bush has put on television commercials to counter Kemp's message. "I'm told some people are out there telling you that I'm for raising taxes," Bush, wearing a bright red ski jacket, says in one spot. "They've got it wrong. . . . By the way, I'm totally opposed to an oil import fee, too."

No longer in single digits, Kemp has broken away from the other lower tier candidates -- former Delaware governor Pierre S. (Pete) du Pont IV, former secretary of state Alexander M. Haig Jr. and former television evangelist Pat Robertson.

A Los Angeles Times poll this month put Kemp in a solid third place in New Hampshire with 18 percent of the vote, only 4 percentage points behind Dole. A poll commissioned by WBZ-TV in Boston and broadcast last night gave Kemp 11 percent, double his standing in December. Bush, at 40 percent, and Dole, with 18 percent, remained static in the survey.

Even Kemp's rivals concede there is movement here for the nine-term New York congressman. "His ads have paid off," said David M. Carney, deputy chief of staff to Gov. John H. Sununu (R), Bush's New Hampshire campaign chairman. "He's out of the third tier and on his way to fighting for the first tier."

Ron Kaufman, Bush's northeast political director, said the Kemp "surge" has not shaken support for either Bush or Dole. According to Kaufman and Gerry Chervinsky, who conducted the WBZ-TV poll, New Hampshire's most conservative Republicans, after months of dissatisfaction and indecision over the available alternatives to Bush and Dole, are beginning to coalesce behind Kemp.

"For the first time in the 10 years that Jack Kemp has been working New Hampshire, the far right of the party, which had no place to go, is kind of holding its nose and going home," Kaufman said.

However, a conservative base built on negative assaults on the two leaders is likely to carry Kemp only so far. His press secretary, John Buckley, said Kemp must finish at least second in New Hampshire to keep alive a campaign that was deeply in debt until it received federal matching funds this month. But to do that, Kemp first will have to avert disaster in the Feb. 8 Iowa caucuses, where he is believed to be in a tight race for third place with Robertson and Robertson's "invisible army" of evangelical Christian supporters.

Kemp and his aides argue that a "respectable" showing in Iowa, even a "tight" fourth-place finish to Robertson, would be enough. Paul Young, Kemp's New Hampshire campaign director, goes along with that reasoning, although he does not sound entirely convinced.

"It makes it tougher," Young said of a fourth-place finish by Kemp in Iowa. "It doesn't make it impossible, but it makes it tougher."

At a minimum, Kemp's late rally here has allowed him to elbow his way into the GOP campaign dialogue, which has been dominated by Bush and Dole speaking to and about each other. Dole, who has gone unchallenged as the only presumed barrier to a Bush nomination, has begun to take notice. He accused Kemp last week of distorting his record on Social Security and the oil import fee. One of his key New Hampshire strategists, Thomas D. Rath, said the Dole campaign "won't leave {Kemp's attacks} out there unanswered."

Like his counterparts in the Bush camp, Rath sees Kemp's late move in the polls here as "short-lived because it's based entirely on the negatives." Moreover, Rath argued, effective attacks on Bush and Dole in New Hampshire do nothing to solve Kemp's most immediate problem, which lies 1,000 miles to the west in Iowa.

"Jack Kemp should remember that most of the time when you throw the bomb at the end of the game, it falls incomplete," he said.

Staff writer Lloyd Grove contributed to this report.