PAWTUCKET, R.I. (AP) _ President Clinton picked at chinks in Republican armor on Social Security today before an audience of senior citizens, one of the Democratic Party's most loyal constituencies.

''Some of you find it hard to believe that anybody, even a conservative Republican, would propose a plan that would cut Social Security benefits,'' Clinton told elderly supporters at the Portuguese Social Club here. ''It's hard to believe, but it's true.''

The president recited various GOP candidates' past and present musings on whether to privatize Social Security, make it voluntary, phase it out or raise the retirement age.

And he repeated the administration's assertion that Republicans would have to cut Social Security by 20 percent to keep their ''Contract with America'' - pledges to increase defense spending, cut taxes, reform welfare and balance the budget, among other things.

''That's $2,000 a Social Security recipient a year. That's it. That is the only way you can do it,'' Clinton said, unless you cut everything except Social Security 30 percent or ditch the promises as soon as you're elected.

Clinton's day in Rhode Island, following appearances Tuesday in Cleveland and Detroit, included a rally and dinner in Providence. He travels to New York and four other states through the weekend in a last-minute round of appearances to raise money and energize Democrats to turn out.

The stakes are high for Clinton and his party: Governors' offices in the nation's biggest states are on the ballot; while in Congress, Republicans are challenging Democratic control of both the Senate and the House.

State Sen. Myrth York, the Rhode Island gubernatorial nominee, appeared to be in a dead heat with Republican Lincoln Almond last week when Clinton was originally scheduled to visit. But his trip to the Middle East forced a postponement and, in the meantime, two new polls came out showing York well behind Almond - a former prosecutor who campaigned here Tuesday with New York Mayor Rudolph Giuliani, a former Justice Department colleague.

The Democratic Senate candidate, Linda Kushner, is nowhere near closing in on veteran GOP Sen. John Chafee, who in fact won praise from Clinton Tuesday for his bipartisanship on crime and health bills.

The party's House candidates are in better shape. Rep. Jack Reed is expected to win re-election and state legislator Patrick Kennedy, Massachusetts Sen. Edward Kennedy's son, is well ahead of his Republican opponent for an open seat.

In two appearances Tuesday that the White House billed as get-out-the-vote rallies, Clinton depicted the Republicans as trying to ''throw a blanket over what we've done the last 21 months.''

Ticking off the accomplishments of his first two years in office - more than 4 million new jobs created, deficit cuts, tax cuts for the working poor, passage of a crime bill - he said: ''We will not turn back. No, no, we're going forward.''

He told an appreciative audience in a Cleveland church that Republicans killed off several other measures in the final days of Congress, including a lobbying reform measure and a campaign finance bill. ''They want to kill things and then blame us for not having them pass,'' he said.

The stops in Michigan and Ohio were designed principally to boost the chances of two embattled Senate candidates, Rep. Bob Carr and Joel Hyatt.

Carr, locked in a tight race with Republican Spencer Abraham, seemed to seek some political distance between himself and Clinton on an earlier presidential visit to a Michigan auto plant. This time, at a rally that featured a balloon drop, and several busloads of children driven to the hall, he said, ''Mr. President, we welcome you,'' and applauded heartily when they appeared together.

Clinton later spoke at a fund-raiser for the congressman.

The political subtext was different in Ohio, where party officials concede Hyatt is in an uphill contest against Lt. Gov. Mike DeWine in the race to succeed Hyatt's father-in-law, Democrat Howard Metzenbaum.

Unlike Michigan, where Carr, the state's two incumbent senators and numerous other Democrats joined Clinton on the podium, the only politicians on the pulpit with Clinton in Cleveland were Rep. Louis Stokes and Mayor Michael White.

Hyatt sat in the front row of the audience, and stood and waved to the audience when Clinton called for his election.

Clinton put in a plug for Democratic congressmen running in nearby districts.