Sen. Bill Bradley (D-N.J.) is a man with a mission. He has been roaring around the Hill, warning fellow Democrats that Ronald Reagan is coming.

Next week, the president will deliver his State of the Union address, focusing -- his aides say -- on the issue of tax simplification and reform. This week, Bradley and his House partner, Rep. Richard Gephardt (D-Mo.), are reintroducing their "Fair Tax Act," the modified flat-tax proposal that launched this latest round of interest in tax reform.

All the flat-taxers say they want to work together across party lines for the goals of tax simplification, base-broadening and rate reduction. That is what the new secretary of the Treasury, James A. Baker III, described as the president's posture, when he testified last week at his confirmation hearings before the Senate Finance Committee.

That is what the sponsors of the main Republican variant on the Bradley-Gephardt bill, Sen. Bob Kasten (R-Wis.) and Rep. Jack Kemp (R-N.Y.), say. And it is what Bradley and Gephardt say too. But these men are all politicians, and the question of personal and party credit for this tax-reform effort is not one they can afford to ignore.

Bradley and Gephardt tried to make the case last August to Democratic presidential nominee Walter Mondale that he should try to get out front on the issue by making it a central part of his campaign. Mondale chose instead to propose higher taxes on upper-income families and corporations -- with results that are well-known.

These past couple of weeks, Bradley has been pleading with Democratic congressional leaders not to miss another opportunity to involve their party conspicuously in the drive to simplify the tax system and reduce rates. As with Mondale, it is not an easy sell.

Most of the provisions now in the complex Internal Revenue Code were put there during the long span of years, from 1954 through 1980, when Democrats controlled both the House and the Senate. Those provisions were put there at the behest of -- and in aid of -- constituencies of importance to Democratic legislators, whether they benefited oil and real-estate operators seeking fast write-offs, or elderly pensioners seeking exemption for their Social Security benefits, or union leaders craving shelter for the fringe benefits they negotiated in contracts.

To expect the authors of these interest-group provisions to lead the fight for their repeal is a contradiction of human nature. Bradley is encountering predictably strong resistance from the Democratic power brokers on the Finance and Ways and Means committees. But he has equally powerful arguments, for he understands that this issue poses a real test of the Democrats' ability to adapt to the changing political environment.

In an interview the other day, the recently reelected senator said: "This issue offers a remarkable opportunity for the Democrats to identify themselves simultaneously with economic growth and individual equity. It is our chance to be for fairness, in the way that most people really see the fairness issue, by doing something to remedy a (tax) system they think is unfair.

"It is our chance to get rid of that special-interest issue that dogged the national ticket in the last campaign. It lets us be for the general interest -- for the 70 percent of the people who would pay the same or less in taxes, under our proposal -- and against the loophole lobbies who are the ones resisting this change."

But this issue is as much of a threat as an opportunity to the Democrats, Bradley said. "If the president is bold on this issue, while we are timid, it could be the realigning issue. It is the issue on which the Democrats who voted for Reagan in 1984 on cultural or social or feel-good issues could find a strong economic interest in continuing to vote Republican."

I do not think Bradley exaggerates the potential of this issue. The conventional wisdom in Washington is that Reagan will reject the parts of the Treasury tax-reform proposal (made public in December) that would cost some corporations and some wealthy individuals their favorite write-offs.

The cynics say that the former General Electric spokesman, now in the White House, will do nothing to disturb a tax code under which G.E. has paid no corporate income tax the last three years. But I think they misjudge and underestimate this president, whose first political hero was not General Bullmoose but Franklin D. Roosevelt.

Roosevelt was a patrician, denounced in the clubs as a "traitor to his class." But he made the Democratic Party the majority party for a half-century. Reagan will endure similar epithets from corporate board rooms if he can make the Republican Party the new majority party by doing what he loves to do anyway -- cutting tax rates for most Americans.

Bill Bradley's warning is one the Democrats cannot afford to ignore.