Most Americans view Nancy Reagan's activity in the fight against drug abuse as sincerely motivated, but many nevertheless feel that her appearances at drug rehabilitation centers are mainly part of a drive to gain better publicity for herself and her husband.

Overall, Mrs. Reagan appears to be viewed slightly more favorably by the public than she was before she began her highly publicized meetings with young people being treated for drug abuse last February.

At the same time, however, the country continues to be sharply split on whether the first lady and her husband set a good model for the nation in their personal style of living.

These are the chief findings of a national Washington Post telephone poll on Americans' attitudes toward Mrs. Reagan. The poll findings suggest that many citizens view Mrs. Reagan, at least in part, through the prism of political partisanship, with Republicans overwhelmingly supporting her but Democrats and independents tending to be somewhat critical.

For example, when asked if Mrs. Reagan visited drug centers "mostly to get better publicity for herself and her husband or mostly because she wants to help fight drug addiction," a substantial majority of Republicans interviewed--65 percent--say her aim is mostly to fight addiction. But only a minority among the rest of the population--41 percent for Democrats, 47 percent for independents--feel that way.

Overall, 49 percent say her motivation is to fight addiction, and 28 percent say it is to gain better publicity. Another 12 percent say she does it for both reasons, and 11 percent express no opinion.

The same pattern holds in response to whether citizens have a generally favorable or unfavorable impression toward Mrs. Reagan. Fifty-six percent say they have a favorable impression, 23 percent report an unfavorable one, and 21 percent express no opinion. Hardly any Republicans--only 9 percent--say they have an unfavorable impression, compared with 30 percent of Democrats and 25 percent of independents.

The "favorable impressions" were up slightly from the 51 percent expressing that view in a November 1981 Washington Post-ABC News nationwide poll. Unchanged from that earlier poll was the 23 percent "unfavorable" rating.

A third question in the new poll was this: "Overall, would you say Ronald and Nancy Reagan set a good model for the country in their personal style of living, or not?" Fifty-one percent say the Reagans set a good model, 38 percent say they do not, and 11 percent offer no opinion.

Translated into numbers, that finding suggests that as many as 60 million Americans find fault with the Reagans' personal life style. The figures are virtually the same as those in a Post-ABC News poll in May 1982, when 52 percent said the Reagans set a good model, 38 percent said they did not, and 10 percent expressed no opinion.

The new poll consisted of interviews with 1,167 adults, selected at random, from Jan. 4 through Jan. 7. A poll that size has a theoretical margin of sampling error of about 3 percent.