On the floor of Madison Square Garden the other evening, John Gilgun, a Democratic state senator from Central Falls, R.I., was telling a passerby how it is for Jimmy Carter.

"I represents the most Democratic city in the most Democratic state in the country," he said, "and I will tell you that if the election were held today, Jimmy Carter would not carrry Central Falls.

"Everywhere I go," Gilgun said, "it's like a record: 'I've never voted Republican in my life, but I can't vote for Carter.' They're upset with unemployment, inflation and the hostages. The Billy business bothered them. And they just don't like him."

As Gilgun, a Kennedy delegate, talked, three other Rhode Island politicians gathered. State Sen. Gloria Kennedy Fleck of Warwick said, "I'm worried for the whole ticket. People feel frustrated, and the country wants a change. I think the Democrats are in serious trouble."

"State Sen. Richard A. Licht of Providence chimed in: "It's a lack of leadership and competence that bothers people."

A. Leo Cuisse, a candidate for the state Senate, added: "I'm scared to death Carter will hurt me."

This conversation was remarkable in only one sense: Rhode Island is not only a traditionally Democratic stronghold, it is also the state that gave Carter his ninth biggest majority in 1976, a healthy 55.4 percent of the vote.

A July poll taken by the Opinion Research Corp. and WJAR-TV in Providence showed Carter running third in Rhode Island, with Ronald Reagan having 28 percent, John B. Anderson 26 and Carter 22.

It illustrates the point made by Democratic pollster Peter D. Hart and acknowledged by Carter campaign planners: as the race begins, Carter is trailing in many of the states he has to carry -- and in some by much worse margins than the Rhode Island poll shows.

While Carter is within relatively easy striking distance of Reagan in overall national polls -- trailing by 14 points in the most recent Gallup survey -- his electoral college picture looks much worse.

Here are some examples: In New York, a July poll by Roger Seasonwein and Associates had Reagan 41 percent, Carter 20 and Anderson 19.

In Massachussets, a late-June Becker Research Corp. poll for The Worchester Telegraph had Reagan 33 percent, Anderson 31 percent, Carter 19.

In Texas, a July poll by the Austin American Statesman and Texas Monthly had Reagan 49, Carter 30, and Anderson 11.

Those three states alone have 81 electoral votes -- all of them in Carter's column in 1976 and all looking vulnerable.

Talks with dozens of delegates and party officials here this week illustrate the weakness of Carter in the traditional Democratic base and the challenge he faces in assembling and electoral college majority.

In Pennsylvania, state Auditor General Al Benedict, the highest-ranking Democratic official, said, "Right now, I don't think he [Carter] has got any strongholds . . . We've gotg a lot of work to do."

In West Virginia Gov. John D. (Jay) Rockefeller IV said, "I think Carter can carry my state, but it's going to be this close -- 50 or 52 percent. It's no sweep." In 1976, it was a sweep -- 58 percent.

In Ohio, Bill Casstevens, regional director of the United Auto Workers, said, "It's salvageable but it will take a lot of work . . . He's going to have to do something about the economy."

In a survey conducted by U.S. News and World Report magazine, the Democratic governors of Florida, Kentucky and Mississippi said Reagan was currently leading in their states. All three were carried by Carter in 1976. c

The heart of Carter's electoral college problem is Reagan's strength in the West and the erosion in Carter's 1976 southern base. Hawaii was the only western state Carter carried in 1976, and it is the only one he is favored to carry this year.

Reagan has a bedrock 118 votes in his column from west of the Mississippi. With such additional Republican states as Indiana, Virginia, New Hampshire and Vermont (all of which Carter lost to Ford) his base is about 150 of the 270 electoral votes needed for victory.

By contrast, Carter can count with some assurance on only about 50 to 75 electoral votes -- and that is probably a generous estimate.

The disparity affects not only the chances of winning but also the strategies of the two campaigns. Carter aides here said they were not overly concerned about polls and other estimates showing Carter shaky in such staunch Democratic states as Rhode Island, Massachussets or West Virginia, because the polls were taken in the "halo" of Reagan's nomination period and at a time when Carter's popularity was scraping its all-time lows.

Speaking of these states, Hawaii and Vice President Mondale's Minnesota, one official said, "We just can't spend much time and effort to carry them. We have to rely on the Democratic traditions somewhere. If we're in bad shape there on Election Day, we'll be wiped out nationally."

But the same official conceded that the disparity in political bases posed a serious problem for Carter -- in leaving Reagan free to concentrate his campaigning on a relatively few states, while Carter has to spread himself thin.

For strategic purposes, the Carter campaign team has analyzed the coming contest as if it were operating separate deffensive and offensive teams.

The offensive strategy is aimed at winning one or more of eight states Carter losts to Ford in 1976: Maine, Connecticut, New Jersey, Michigan, Illinois, Washington, Oregon and California -- with a total of 130 electoral votes.

The first three are on the list because of what Carter pollster Patrick Caddell refers to as "Reagan's eastern problem," a set of polls suggesting that the Californian is as out-of-touch with the Eastern Seaboard as Carter is with the mountain and plains states.

But Reagan's running mate, George Bush, has personal and family ties to Connecticut and Maine and won as handsomely in the Michigan GOP primary as Reagan did in his native state of Illinois.

The West Coast states are regarded as targets for different reasons -- a shift of 30,000 votes would have given Carter Washington in 1976, and he could have carried Oregon with a shift of fewer than 1,000 votes.

In California, where most of the Democratic leaders regard Carter's position as hopeless, Caddell professes to see signs of Reagan vulnerability in the polls. His faults are better known there than anywhere else, the argument goes. Besides, as another official put it, "If you're running for president, you can't afford to write off completely a state with 45 electoral votes."

For the most part, the Carter planners assume that Anderson's strength will ebb as the Nov. 4 election day approaches. They welcome that prospect as improving Carter's chances in most closely contested states.

But, perversely, they also argue that Anderson may hold the key to upsetting Reagan in California, if enough moderate Republicans and independents desert Reagan for the Illinois congressman.

The defensive half of the Carter strategy concentrates on 10 states with 185 electoral votes that Carter carried last time but is uncertain of winning now. Five of the states are in the South -- Alabama, Mississippi, Florida, Louisiana and Texas -- and they will see and hear a great deal from Carter about regional pride in a Dixie president.

The other five states are in the Middlewest and East -- Missouri, New York, Ohio, Pennsylvania and Wisconsin -- and there Mondale's ties to unions, teachers and other liberal groups will be heavily exploited.

The first step to raise funds to finance the $4.6 million effort the Democratic National Committee is allowed to spend as a supplement to the $29.4 million in tax funds the Carter-Mondale Committee will pick up next week, and to encourage state Democratic parties to raise and spend as much as possible on volunteer phone banks, campaign materials and voter registration.

In all these financial and organizational aspects, the Democrats acknowledge they are playing catch-up to the GOP, but now that their convention is over, their efforts will accelerate.

"You would be safe in saying," one official commented wryly, "that we know we have a lot of work to do."