John B. Anderson, who announced two weeks ago that he plans to run as a third-party candidate for president in 1984, could emerge as a spoiler who would keep the Democrats from regaining the White House, according to a new Washington Post-ABC News public opinion poll.

Anderson's present support from one of every eight voters is enough, the poll shows, to hurt seriously either of the two leading Democrats, former vice president Walter F. Mondale and Sen. John Glenn (D-Ohio).

Support for Mondale and Glenn has increased in recent weeks, and both are running ahead of President Reagan in trial heats in the poll. But the lead of each disappears in a three-way race, with Anderson siphoning almost all his support from the Democratic candidate and virtually none from Reagan.

As in other recent polls, Glenn, bolstered by support from independent voters, does somewhat better than Mondale when pitted against Reagan. But the former vice president shows considerably more strength among the Democratic rank and file.

Mondale leads by a substantial margin over Glenn as the first choice for the party's nomination, and 70 percent of all Democrats list Mondale as no worse than their second choice.

By comparison, 49 percent of Democrats list Glenn as their first or second choice. The poll, conducted last Wednesday through Sunday, also suggests that one of the key elements in the 1984 election, should Reagan run again, will be how candidates deal with a public whose political and economic outlook is sharply divided along income lines.

Those with household incomes of more than $20,000 a year--roughly half the voters--are generally optimistic that the national economy has turned the corner and tend to give Reagan high grades for his handling of the presidency.

The other half, below $20,000 a year, however, tend to doubt that the economy is improving, give Reagan negative ratings on most issues and generally regard him as a rich man's president.

In political terms, this puts either of the two leading Democratic candidates substantially ahead of Reagan among voters with low to moderate incomes, but both trail Reagan among the other half with higher incomes.

Overall, the poll shows Mondale now leading Reagan by 49 to 44 percent among registered voters, a turnaround since mid-May, when a Post-ABC News poll showed the Minnesotan trailing by 47 to 42. But with Anderson included as a third candidate, Mondale and Reagan are tied--39 to 39--with Anderson drawing 13 percent. Glenn now holds a wide lead over Reagan in a two-way race--52 to 40 percent among registered voters--after being even at 44 to 44 in May.

But with Anderson included, it again becomes a virtual dead heat: 40 percent for Glenn, 39 percent for Reagan and 13 percent for Anderson.

Anderson received 6.7 percent of the national vote for president as an independent candidate in 1980. Despite his background as a longtime Republican congressman, most of his support then came from Democrats and independents.

But had Jimmy Carter taken all of Anderson's votes, he still would not have defeated Reagan, who won with 51 percent. In an interview with Washington Post staff writer Bill Peterson two weeks ago, Anderson said he is drafting a set of principles for a third political party which he hopes to get off the ground by fall.

He said he plans to run despite the belief that a third-party candidate could not win.

"The emphasis has to be on establishing a new national debate whether you win the election or not," he said. Calling the two major parties "captives of special interests," he argued that "somebody ought to break the gridlock."

The Post-ABC News poll also attempted to test the political strength of Jesse Jackson, the black activist leader who is seeking the Democratic presidential nomination. In a trial heat between Reagan and Jackson as the Democratic candidate, Reagan leads, 55 to 29 among registered voters, according to the poll.

Jackson trails far behind Mondale and Glenn as the preferred nominee among Democratic voters, but he leads the rest of the pack. The poll shows 42 percent for Mondale, 26 percent for Glenn, 8 percent for Jackson, 7 percent for Sen. Alan Cranston (D-Calif.), 3 percent for former Florida governor Reubin Askew, 2 percent for Sen. Gary Hart (D-Colo.) and 1 percent for Sen. Ernest F. Hollings (D-S.C.).

On the Republican side, the favored nominee should Reagan decide not to run is Vice President Bush, supported by 52 percent of the Republican voters interviewed.

Placing second is Sen. Howard H. Baker Jr. (R-Tenn.), with 25 percent, followed by Sen. Robert J. Dole (R-Kan.) with 10 percent and Rep. Jack Kemp (R-N.Y.) with 7 percent.

Polling assistant Kenneth E. John contributed to this report.