"IN A REAL sense," Jesse Jackson said recently, "I'm running every day, every year." On Saturday, before the National Rainbow Coalition in Raleigh, N.C., he made it official: he is running for president in 1988. He is the only 1984 candidate now in this year's contest, he begins with a lead in many polls, and he is the Democrat who seems most certain to be running still when the party convenes in Atlanta next July.

He begins the race this year with much of the same support he had in 1984, but with a new message. Four years ago he was attacking the system, complaining about runoff primaries and Democratic Party rules. But these were the claims of a candidate interested in maximizing his clout, though he could not win a majority of the votes. This year Mr. Jackson is sounding themes he hopes will rally a majority.

Domestically he distrusts free markets: he wants a moratorium on farm foreclosures and attacks big corporations for exporting jobs overseas. On foreign policy he denounces the U.S. invasion of Grenada, aid to the Nicaraguan contras and support of Angolan rebels. He would "break the back of the arms race" by renouncing not only weapons opposed by his Democratic rivals but such systems as the Midgetman and the Stealth bomber, which most of them favor. He wants to beef up the Coast Guard to stop imports of illegal drugs. He continues to rouse black audiences, but he has set up a headquarters in Iowa and speaks to beleaguered farmers and displaced factory workers.

Mr. Jackson evidently believes there's a potential majority made up of those who are in various ways downtrodden: potential, because many are now nonvoters and need to be registered. Skeptics will point out that the Farm Belt is perking up, the industrial states have been recovering for several years, the nation is in its 59th consecutive month of economic growth, and per capita income is at an all-time high. They doubt that, even with an expanded electorate, Mr. Jackson's views of the state of the nation will prove persuasive. Others are far from confident that his soft spot for some left-wing and Third World tyrants and his insensitivity to Jewish concerns are things of the past.

Such doubts and Jesse Jackson's beliefs will both be tested in the campaign to come.