Americans are split sharply over the compromise plan to alter funding and benefits of the Social Security System despite the praise that President Reagan and leading Democrats have lavished on it, according to a Washington Post-ABC News poll.

Although the plan has been hailed as the salvation of the system, most people say they continue to doubt that the Social Security program will exist when they retire.

A majority or plurality of citizens opposes each of the three aspects of the plan that call for increasing Social Security taxes. A majority favors the parts of the plan that require no added cost, such as increasing benefits for those who delay their retirement past 65, and the inclusion of new federal workers in the system.

A majority also supports a highly controversial recommendation that would delay until January, 1984, an increase in Social Security benefits that is scheduled for July, 1983.

In his State of the Union address Tuesday, Reagan emphasized the bipartisan nature of the proposals, and said the commission that he and congressional leaders of both political parties appointed had "accomplished the seemingly impossible" by devising a compromise plan after "months of debate and deadlock."

Many citizens, however, apparently view the plan more as Reagan's solution than as a bipartisan Democratic and Republican program. The poll shows that those who support Reagan's handling of Social Security strongly endorse each of the key recommendations, and those critical of Reagan's handling tend to oppose each.

Overall, 56 percent in the poll said they disapprove of Reagan's handling of Social Security's financial problems, and 32 percent said they approve, a gain for him since last October, when 60 percent in a Post-ABC News poll disapproved and 26 percent approved. The new figures suggest that Reagan still is bleeding from the wounds the debate over Social Security inflicted, but that the hemorrhaging may have stopped.

The poll included a dozen questions on attitudes toward Social Security, and shows the public overwhelmingly endorsing the system as it exists, but looking nervously at proposed changes. Almost nine in 10 said that current benefits paid to retirees are either "too low" or "about right," and only 8 percent said benefits are "too high."

Similarly, eight in 10 said that current payroll deductions for Social Security are either "about right" or "too high," and only one in 10 said they are too low. These findings suggest the extreme sensitivity political leaders must deal with in trying either to reduce benefits or to increase Social Security taxes.

When forced to choose between increasing taxes or lowering benefits, the public overwhelmingly voted to leave benefits intact. Fifty-eight percent preferred raising taxes, 21 percent selected cutting benefits, 3 percent favored a little of both, 12 percent said they would do neither, and 6 percent offered no opinion.

But other responses in the poll strongly suggest that most citizens see increased taxes only as a last resort for rescuing the system. A majority of 55 percent opposed one of the chief features of the proposal, increasing payroll taxes for Social Security in 1984 instead of 1985, as had been scheduled. Only 39 percent approved speeding up that tax increase, and 6 percent expressed no opinion.

In addition, the public is divided closely over whether retirees with substantial outside income should pay taxes on part of their Social Security benefits, with 49 percent opposed, 46 percent in favor, and 5 percent offering no opinion.

And, despite the relatively small proportion of people who run their own businesses, 51 percent opposed increasing Social Security taxes for the self-employed while 40 percent approved and 9 percent were undecided.

Fifty-two percent supported the recommendation to delay the scheduled increase in benefits from July until next January. Forty-three percent opposed it, and 5 percent offered no opinion. The acceptance of that provision in the face of keen opposition to overall benefit cuts suggests that many citizens do not equate the delay with a reduction in benefits, although it has that effect for people now receiving them.

The poll was conducted from Jan. 18 to Jan. 23, beginning several days after the commission arrived at its compromise. Although the commission's recommendations were publicized widely and praised by political leaders as a means of preserving the Social Security System well into the future, a majority of the public fails to share in that enthusiasm.

Asked whether Social Security "will exist or not when you or your spouse retire," 55 percent of the people under 60 said they think it will not exist. That represents only slightly less pessimism than uncovered in a January, 1982, Post-ABC News poll, when 59 percent of those under the age of 60 said they felt that Social Security would be defunct by the time they or their spouses would be eligible for it.