MANCHESTER, N.H., FEB. 15 -- Vice President Bush and Senate Minority Leader Robert J. Dole (R-Kan.) made their final campaign appeals today before a critical showdown that is likely to shape the tone and content of the Republican presidential contest from now until the GOP national convention in New Orleans in August.

On the eve of Tuesday's New Hampshire primary, public opinion polls and the assessments of campaign professionals had the race a virtual dead heat. In seven days of campaigning since Dole won the Iowa caucuses and Bush finished third behind former television evangelist Pat Robertson, the vice president's once-substantial lead here has vanished, putting victory within Dole's grasp -- but not certainty.

Tracking polls by The Washington Post and ABC News of 405 likely Republican primary voters today had Dole and Bush even at 32 percent.

The same survey showed Rep. Jack Kemp (R-N.Y.) the choice of 12 percent of likely primary voters, former Delaware governor Pierre S. (Pete) du Pont IV with 10 percent support and Robertson with 8 percent.

Tracking polls of a total of 969 likely GOP voters over the Saturday-through-Monday period showed a similarly tight race. The three-day tracking gave Dole 33 percent, Bush 30 percent, Kemp 13 percent, du Pont 10 percent and Robertson 8 percent. The poll has a margin of sampling error of plus or minus 4 percent.

On the Democratic side, as the seven contenders finished campaigning, Massachusetts Gov. Michael S. Dukakis anticipated a large victory and the fight for second place remained extremely tight between Rep. Richard A. Gephardt (Mo.) and Sen. Paul Simon (Ill.). {Details, Page A7.}

Among the Republicans, a second consecutive Dole win Tuesday would firmly establish him as the GOP front-runner and leave Bush in need of a dramatic recovery in South Carolina on March 5 and in the March 8 "Super Tuesday" contests, concentrated in the South.

But a Bush win -- even a narrow one -- would give the vice president and his campaign organization breathing space, probably assuring a long and bitter struggle for the nomination.

Similarly, Tuesday's primary represents a key test of Robertson's appeal beyond his Christian evangelical base and a possible last stand for the Kemp and du Pont campaigns.

An irritable Robertson spent his last New Hampshire campaign day on the defensive, fending off questions about his assertion during a televised debate Sunday that the Soviet Union has placed SS4 and SS5 intermediate-range missiles in Cuba. The White House, State Department and Pentagon have dismissed the assertion.

Robertson's strong showing in Iowa and other early caucus states has shaken the Republican establishment here, a development that could benefit Dole if he is seen as more likely than Bush to turn back the Robertson challenge. New Hampshire is the first primary contest of the presidential nominating process and should provide clues to the extent as well as the intensity of Robertson's support.

In what has evolved into a separate, second-tier contest, Robertson is locked in a close race with Kemp and du Pont for third place and the right to claim the mantle as the true "conservative alternative" to Bush and Dole. But unlike his two closest rivals, Robertson has the financial and organizational resources to survive a disappointing showing here.

Bush spent his last campaign day here attacking Dole's budget proposals and invoking the support of the spiritual father of the conservative movement in the GOP, former senator Barry Goldwater of Arizona.

Goldwater appeared at Bush's side at a news conference in Nashua and in a five-minute television commercial that was broadcast tonight. In the ad, Goldwater, the 1964 GOP standard-bearer who lost in a landslide, described Bush as "the best-qualified candidate of my lifetime -- other than me, George."

Asked at the news conference why he had not endorsed a "more conservative" candidate than Bush, the 79-year-old Goldwater replied in customary style:

"Endorse a more conservative candidate than Mr. Bush? Who the hell is it?"

Speaking to an elderly audience at the Hunt Community Home in Nashua earlier today, Bush assailed Dole's call for a federal spending freeze, contrasting it with what he called the more flexible "Bush Leadership Freeze" that he claimed would produce a balanced budget by 1993.

Bush strategists made clear that they are counting on the organizational muscle of Bush's New Hampshire chairman, Gov. John H. Sununu (R), to tip the balance if the race remains as close as it appears. Ron Kaufman, Bush's Northeast political director, has been telling reporters for months that the organization was built to withstand a "worst-case scenario," an apt description of what happened to Bush in Iowa.

Meanwhile, Dole sought to fire up his organization, telling hundreds of volunteers here: "Winning isn't everything, but let's try it tomorrow and see how it feels."

Dole and his advisers also sought to deflect charges by Kemp and du Pont that he would raise taxes to reduce the federal deficit. In Dover, Dole repeated his pledge not to increase personal or corporate income taxes while his New Hampshire chairman, Sen. Warren B. Rudman (R), said Dole's record had been distorted by "fringe candidates."

Having erased a double-digit Bush lead in the polls, Dole strategists were ready to declare victory today. "If we lose this race, it will be by an eyelash," Rudman said. "That's a victory for us."

Richard Wirthlin, Dole's pollster, said internal campaign surveys put Dole only slightly ahead of Bush but that other measurements from the polls "add up to a good night's sleep" on the eve of the primary.

William E. Brock III, Dole's national campaign chairman, said Bush's swift tumble from his once-commanding lead here indicated a fundamental weakness in the Bush candidacy.

"To have a campaign fall out from under you like that says something devastating," Brock said.

With the polls about to open in New Hampshire, the Republican contenders began looking ahead. Dole is scheduled to return to Washington late Tuesday night and leave the next day on an extensive campaign trip, much of it in the South. Bush is to return to Washington by Wednesday before heading south.

Brock said the South -- which, like New Hampshire, has been seen as a Bush stronghold -- now offers "tremendous opportunity" for Dole. He said that regardless of the New Hampshire outcome, the Bush-Dole contest will go on.

"He's a good candidate and a good man and he's got several million dollars in the bank," Brock said of the vice president. "He's not going to give that money back."