Reps. Beryl F. Anthony Jr. (D-Ark.) and Charles Hatcher (D-Ga.) should have been listed in Sunday's Post as members of the Conservative Democratic Forum in the House. The congressmen, recent additions to the group, were not included on the forum's official membership list.

Two decades after the old congressional "Boll Weevils" began to lose their power, the South has risen again on Capitol Hill.

When the House opens its floor fight this week on President Reagan's budget package, the fulcrum of political power will rest on the Deep South -- specifically, on some 40 conservative Democrats whose votes most likely will be decisive in the confrontation between the Republican president and the Democratic House leadership.

Who controls the House? The swing votes will decide that.

These southerners, who recognize and relish their pivotal position, have organized into a group formally titled the "Conservative Democratic Forum."

Informally, though, the southerners like to call themselves the Boll Weevils -- the team used pejoratively to describe the bloc of veteran southern Democrats who dominated Congress for who decades after World War II.

Except for common geography, though, the new Boll Weevils are a strikingly different breed from their forebears. They are younger, more videogenic, more concerned about the news media, less ideological, more moderate on racial issues. And they are also less secure politically -- elected from Democratic districts that might well go Republican.

The old southern bloc, led by men like Sam Rayburn and George Mahon of Texas, Richard Russell of Georgia and James O. Eastland of Mississippi, had a basic respect for party lines and parliamentary hierarchy.

They recognized congressional seniority as the source of authority in Congress. By winning term after term from safe Democratic districts, they used seniority to achieve power and prominence in both houses of Congress.

The new Boll Weevils, in contrast, have no clear leaders, and little individual power or prominence. And they exhibit a noticeably limited sense of allegiance to their party and its leaders.

Like all politicians, their first impulse is survival and, in today's South, that often has little to do with the interests of the Democratic Party.

"People [in the new southern bloc] don't vote by party line," said G. V. (Sonny) Montgomery, a dapper, gray-haired Mississippian who is one of the group's senior members. "A congressman's final vote is in the interest of his district." Most southern districts, as the Democratic Boll Weevils are acutely aware, went for Ronald Reagan last November.

For these reasons, Republicans are counting on the southern Democrats to provide the margin of victory when Reagan's budget and the Democrats' alternative version come head-to-head on the House floor.

Preliminary head counts suggest that virtually all of the 191 House Republicans will support the administration plan.White House sources expect no more than a half-dozen GOP defectors.

The Democratic leadership thinks it can count on about 200 safe Democratic votes for its budget proposal. If these predictions hold, the showdown will be won by the side that can capture more votes from the swing bloc -- the southerners.

This strategic situation explains much of the maneuvering over the budget resolution before the House. The Democratic version was designed to win over the Boll Weevils without losing the moderates and liberals who make up most of the House majority.

Thus, while it would cut President Reagan's defense spending figures, it includes more money for veterans' programs, a key interest of Montgomery and other southern Democrats.

As a counterploy, Reagan agreed to "refine" his budget along lines proposed by Rep. Phil Gramm, a conservative Democrat from the central Texas community of College Station. He was voted with the Republicans in the House Budget Committee.

Although the upcoming budget vote marks the first time the Democratic conservatives have held the balance of power on a key vote, the members of the group have recognized for some time that, despite their minimal seniority, they could hold the controlling position in the House.

"Seven or eight fellows would sit together during roll calls, toward the back of the House," recalls Rep. W. G. (Bill) Hefner, a quiet, bespectacled 51-year-old from North Carolina. "We'd have a cup of coffee during a break and talk about how disappointed we were with the way things were going. . . . Gradually came the idea, why not have an informal group? . . . Maybe we could put pressure on the leadership."

It was Rep. Charles W. Stenholm, 58, a cotton farmer from Stamford, Tex., who molded these grumbling backbenchers into a "forum."

Stenholm, who came to Congress in 1979, had been a regular participant in those informal discussions, and when he returned after the election last fall he began pushing his soulmates to organize.

"We're people with a conservative philosophy who've been on the losing end of the majority of votes in the last couple of years," he said. The election returns "made it clear that it was in the best interests of the Democratic Party . . . to achieve better representation for the conservative element."

Some of the more fervid conservatives, such as Texas' Gramm, proposed a joint effort with Republicans to oust liberal Thomas P. (Tip) O'Neill Jr. of Massachusetts as House speaker.

Others rejected any such mutiny, but the Boll Weevils did use their collective muscle to win new seats on the most important House committees, including three Budget Committee slots.

With increased clout, they have developed an increasing sense of independence from party discipline. The result is that O'Neill and House Majority Leader Jim Wright of Texas, despite intense lobbying among the conservatives, have won few southern Democratic commitments on the budget issue.

Among those O'Neill spoke to was Gramm, a self-assured, 38-year-old former economics professor. Gramm, in an interview, said that he listened to the speaker, but felt no sense of allegiance to his party's leader.

"If you define the Democratic Party the way the speaker does," Gramm said, "then there are virtually no Democrats in my district. My people think Ronald Reagan is right; they're on his side."

The Democratic leadership got a similar response from Rep. John B. Breaux, a smooth, articulate 37-year-old who has represented Louisiana's Gulf Coast Cajun country in Congress since 1973.

"The Democratic Party [in the House] was not representing our interests," Breaux said. "Out in the hinterlands there is more and more a conservative-liberal split rather than a Democratic-Republican. There isn't strong party affiliation. Fiscal philosophy is the dividing line. If I voted against the Reagan budget . . . people would say Breaux is trying to stop Reagan's effort to bring back fiscal sanity."

On the other hand, the Democratic Conservative Forum also includes members who share the zeal for fiscal conservatism but still believe the Democratic Party better reflects their overall political philosophy.

In this group are "moderate conservatives" like Hefner of North Carolina and Rep. Bill Nelson, a 38-year-old, second-team congressman whose district includes Orlando and Cape Canaveral in Florida. Another of this sort is the forum's only northern member, Samuel S. Stratton, 64, former mayor of Schenectady, N.Y., who has served in the House since 1959.

"Even conservatives draw lines with Republicans," Hefner said. "We believe that government has an obligation to help people less fortunate than we are. . . . If we see we've cut too deeply and people are suffering, then I'll vote to restore those funds."

However, if the Boll Weevils pose a difficult problem for the Democratic leadership, they also constitute a quandary for House Republicans. Some GOP leaders think the party should work closely with the Democratic conservatives to win their votes for Reagan programs. But others think the Boll Weevils should be given no quarter.

"If I were Reagan, I wouldn't have a thing to do with those guys," said Rep. David B. Crane, a conservative Republican from Illinois. "You look at their districts, those ought to be Republican seats. I would say they can go ahead, vote with Tip [O'Neill], and then we'll go into every one of their districts in '82 and say: 'Elect a Republican because this guy blocked the president's program.' And we'll have a majority in the next Congress."

Paul Weyrich, director of the Committee for the Survival of a Free Congress, which backs conservative congressional candidates of both parties, said he expects the Republican leadership to offer conservative Democrats a tacit bargain for the 1982 election.

"I have been talking to Republicans . . . and to business executives who are prepared to put major bucks into the 1982 elctions," Weyrich said. "And there is a sense that if the [conservative Democrats] vote for Reagan in the House, they ought to get a bye in '82. . . . I don't think they can make a public policy statement like that, but the word is being passed."