SEVEN DEMOCRATS are already in the presidential race, but many party activists are still dissatisfied with the choices. Although some of them think that Sam Nunn would be the dream candidate, they may want to think again about whether a Nunn candidacy suits the Democratic Party.

The 48-year-old Georgian, who is chairman of the Senate Armed Services Committee, is best known for his expertise in defense. He has filled the Democrats' credibility gap on military issues and has challenged Reagan administration policies in this area quite effectively. In addition, he has served with distinction in the Senate since 1973, and he is unquestionably bright and well-respected.

But Sam Nunn is also unquestionably conservative. Judging by his voting record, he is more conservative, in fact, than several of his southern Democratic colleagues, such as Dale Bumpers of Arkansas, Ernest F. Hollings of South Carolina and Lawton Chiles of Florida.

When Nunn's domestic record is examined, it is unclear whether he could appeal to the Democratic Party's base, particularly in his native South. In the South, Democrats must balance attempts to pick up conservative white strongholds with efforts to secure one of the party's most reliable sources of support, the black community. The Rev. Jesse Jackson's forceful presence in presidential politics underscores the difficulty for any white candidate. Nunn's conservatism might well cost the party at least as many votes in that region as he would attract.

Furthermore, the very things that make Nunn appealing to southern conservatives could alienate him from Democrats in other parts of the country, who find him out of step with mainstream Democratic philosophy. Here's why Nunn's domestic record, especially on civil rights, may cause him trouble:

Voting Rights. In 1975, Nunn was one of only 13 senators who voted against bringing up legislation to renew the landmark 1965 Voting Rights Act. The act stopped the most obvious forms of voter discrimination and gave the federal government new authority to monitor election practices in states with a history of racial bias. Opponents claimed that the law unfairly targeted the South and infringed on states' rights.

Nunn was an active participant in the 1975 debate, arguing that the legislation would punish the South and end up discouraging rather than encouraging state officials to get more blacks to register to vote. At one point he called the legislation "built-in inequity to seven states in this country." Nunn was also one of 20 senators who voted against ending a filibuster on the bill.

While Nunn eventually voted for final passage of the 1975 bill, he supported most weakening amendments and sponsored one of them.

In 1982, when the law was up for renewal again, Nunn voted in a similar vein. Although he opposed a filibuster this time, he supported several amendments to soften the bill's impact before supporting final passage. The majority of Democrats -- and a substantial number of Republicans including Robert Dole and Nancy Kassebaum of Kansas, Charles E. Grassley and Roger Jepsen of Iowa and Rudy Boschwitz and David Durenberger of Minnesota -- opposed the weakening amendments that Nunn supported.

Fair Housing. Nunn cast one of the key swing votes in December 1980 to continue a filibuster that killed legislation giving the Department of Housing and Urban Development new tools -- fines and the right to issue injunctions -- to fight housing discrimination. Critics said the bill as drafted was too burdensome, wouldn't work and was probably unconstitutional. The majority of Democrats was on the opposite side from Nunn.

Court stripping. During a six-week fight in the fall of 1982, Nunn voted consistently in support of efforts by Jesse Helms, the North Carolina conservative, to make it possible for states to enact laws allowing prayers in public schools or restricting access to abortion. Helms' tactic was to strip federal courts of their authority to hear cases involving challenges to such laws. Helms' allies said there was nothing in the Constitution that prevented Congress from deciding what issues the federal courts could or could not decide, but critics said this was an extraordinary and impermissible encroachment on the federal judiciary. Once again, Nunn parted company with most of his Democratic colleagues who opposed Helms.

The court-stripping votes were tied to procedural matters, as is often the case in Congress. This time it was a tangled parliamentary fight over raising the federal debt ceiling. However, the debate made clear that the procedural votes, which would have ended an anti-Helms filibuster, were tantamount to votes on the merits of the school prayer and abortion issues.

Abortion. In 1983, Nunn supported a proposed constitutional amendment designed to make abortion illegal. It would have overturned the Supreme Court's 1973 Roe v. Wade ruling that made abortion legal nationwide. The amendment failed with most Democrats, but not Nunn, opposing it.

Balanced budget amendment. In 1982 and again in 1986 Nunn supported a constitutional amendment to require a balanced budget. Supporters said the amendment was the only way to make Congress exercise fiscal discipline. Critics said the proposal was a political fig leaf; moreover, if enacted, it would hit hardest at domestic programs, especially those that help the poor. A majority of Democrats opposed the amendment, but Nunn did not.

If Nunn is compared to other Democratic senators over the last six years, he emerges as one of Reagan's most consistent supporters in the party, according to Congressional Quarterly vote studies. The studies measure how often a senator votes with the president when the president has clearly taken a position on an issue.

From 1981 through 1986, Nunn was among the Senate Democrats who supported Reagan most often. In 1983 and 1985 he led Democrats in backing the president, voting with Reagan 64 percent of the time in 1983 and 58 percent of the time in 1985.

Sam Nunn may seem like an attractive national candidate, but only until Democrats really get to know him.

Nadine Cohodas is a senior writer for Congressional Quarterly