The White House is gearing up for its first major political offensive on President Reagan's economic recovery plan, a three-day "southern blitz" aimed at friendly persuasion of conservative Democratic congressmen.

Beginning April 23, four teams of well-known Republicans will fan out throughout the South, holding news conferences and meeting with political and community leaders. The effort, described as "educational" by White House aides, is being directed by Lee Atwater, a deputy of White House political director Lyn Nofziger.

Polls taken for the administration show support of at least 2 to 1 for the president's economic program in the southern congressional districts where such speakers as Vice President Bush, former president Ford, New York Rep. Jack Kemp and Sens. Strom Thurmond (S.C.), Jesse A. Helms (N.C.) and John G. Tower (Tex.) will be appearing.

Because of the White House involvement, this campaign will emphasize the positive, stressing the supposed virtues of the economic plan and making no direct criticisms of the Democrats in whose districts they will speak.

"We want to make it easy for these Democrats to vote for the plan," said one White House aide. "This is not an attempt to embarass or oppose any congressman."

Behind the carrot of friendly persuasion, however, lies the potential club of political opposition in the 1982 elections. White House political strategists are aware of Reagan's enormous popularity in the South, where he runs even stronger than in the rest of the nation, and Republican hopes for further congressional gains are considered highest in this region.

So next week's blitz, even though conducted on the politest of political terms, is a reminder to vulnerable Democrats that they could face serious opposition in the next election if they don't back Reagan on the program that means the most to the president.

Some of the speakers and their aides also will be meeting with key fundraisers and political leaders in the districts they will visit.

"We follow the golden rule, which is that gold rules," said an administration official.

Next week's blitz is timed to occur while congressmen are still in their districts for the Easter recess, on the theory that the incumbents will get the pro-Reagan message from constituents and opinion leaders.

While there will be some differences in emphasis among the various GOP speakers, most of them are expected to make the same "talking points." These are that the economic plan will reduce "waste and fraud" in government while protecting the needy and bolstering the defense budget, and ultimately bringing down inflation.

The speakers also are supposed to stress the importance of Reagan's preferred three-year 30 percent tax-reduction bill preferred by many Democrats.

The House Budget Committee has approved a rival Democratic budget by a vote of 17 to 13, but the White House congressional liaison protection looks forward to victory for the Reagan plan, or most of it, on the House floor.

To achieve this, the White House needs the votes of at least 30 conservative Democrats. Nearly all of them are on next week's blitz list.

"The southerners are the key for us," said a White House aide yesterday. "If they vote for the plan it's going to carry, and if they don't it's going to lose. And we can't win these votes by going to Democratic leaders. We have to go to their districts."