By anyone's standard, Charlie Stenholm is an unlikely Washington power broker. Leaning back, wearing a short-sleeved shirt and bland tie, the west Texas congressman looks as homey as a county agricultural agent. Hardly the sort of fella you'd envision deciding the fate of presidential programs.

But a few weeks ago, Stenholm and his Dixie cohorts were the pivotal force behind President Reagan's stunning House victory on the budget. And they've spent much of the past few weeks at the White House -- conspicuously attending state dinners and ultimately cutting a deal on the administrationhs new tax-reduction package.

The group, known formally as the Conservative Democratic Forum, is the political vehicle for most of the 63 Southern conservatives who defected from Democratic ranks last month to help House Republicans serve up the Reagan budget victory. Stenholm himself is a second-term Democrat.

Put together hastily last autumn as one of the innumerable special interest caucuses in the House, the forum overnight has become the hottest political property in the 97th Congress. Stenholm's only worry is whether its momentum has peaked too soon.

But to many, the real question is, will the Southerners' new coalition with the GOP really last, or will it fall like a bug-ridden cotton plant once the Republicans win their initial victories and start campagining to put their own members in office?

For the moment, Stenholm and his group are riding high.

"We had no earthly idea that things would work out this well," the 43-year-old Stamford, Tex., congressman said last week, recalling the group's modest expectations during its first couple of meetings after last November's Reagan landslide. "All we were hoping for was to get our views known around."

But the forum also has its detractors:

Many House Democrats have begun complaining that the "Boll Weevils," as the Southerners are called, bargained in bad faith bad first by first pressing party leaders to make key concessions on the tax-cut issue and then scurrying, at the first opportunity, to Reagan's side anyway.

Some forum members are concerned their two back-to-back defections -- first on the budget and now on the tax-cut issue -- will prompt mainstream Democrats to write them off, eroding their ability to bargain. Already there are questions: What's the difference between the Weevils and the Republicans?

Finally, Stenholm and other forum leaders concede that the group may find it more difficult to deliver the votes for Reagan's tax-cut bill than it did on the budget isue. Voters themselves are less rabid about tax relief than about budget-balancing. Even the forum's members are split over just how far to go.

The institutionalization of "Weevil Power" in the House is a relatively new phenomenon. Although their was a Southern bloc in the early 1950s and '60s, Dixie Democrats have been silent for most of the past few years. The Conservative Democratic Forum wasn't formed until last November.

To Rep. Ed Jenkins (D-Ga.), a quiet-spoken Georgian who was one of the organization's founders, the forum "was born out of frustration, more than anything else" -- an effort by the Southerners to get the House leadership finally to pay some attention to them.

In the early 1970s, conservative Democrats were pretty much confined to the House woodwork. The party was leaning leftward, with the liberals calling the shots. And there simply weren't enough Republicans in Congress to offer much hope for reviving the old Dixie-GOP coalition.

In the 1976 campaign, it was clear to the conservatives that the electorate had shifted to the right, but the change wasn't reflected in the House Democratic leadership. Recalls Jenkins: "Every time a vote would come up, the leadership would say, 'You people have to yield and vote with the liberals.'"

Over the next four years, the Southerners sat by frustrated while moderate Democrat were defeated. The lesson wasn't lost. When Reagan swept the election in 1980, the conservatives decided it was "time to get the leadership's attention." Ten days after the balloting, the forum held its first meeting.

As Stenholm recalled last week, the post-election arithmetic was indisputable. With 33 new GOP seats, it would take the votes of only 26 Southern Democrats to give the conservatives a majority."It suddenly became very obvious," he says, "that we could possibly affect the course of legislation in the 97th Congress."

The forum began with modest enough ambitions. There already were 23 other congressional caucuses -- the Black Causes, the Steel Caucus, the Women's Caucus, the Northeast-Midwest Caucus. Most are content with being platforms for their member's views. If the CDF did the same, that would be well enough.

The first few weeks of the new Congress brought some modest -- but nevertheless significant -- victories: At the Southerners' urging, the leadership named a half-dozen conservative Democrats to key policy and legislative committees. The Southerners had complained that they weren't fairly represented.

The lineup included Reps. Phil Gramm (D-Tex.) and Bill Hefner (D-N.C.) to the House Budget Committee, Rep. Kent Hance (D-Tex.) to Way and Means and Reps. Bo Ginn (D-Ga.) and Wes Watkins (D-Okla.) to the policy-making Democratic Steering Committee.

But the forum's most stunnig accomplishment came right out of the blue -- in the battle over Congress' new budget resolution last spring:

Gramm, unhappy over a proposed Budget Committee plan that would have cut defense spending too sharply for his tastes, militantly joined with ranking Republican Delbert Latta (Ohio) in drafting a "conservative substitute for the floor fight.

Few thought the coalition had much chance of winning. Substitutes of that sort come up each year -- and usually are soundly defeated. But surprise! -- 63 Democrats joined the cause, and Gramm-Latta, as it was called, passed by an overwhelming 253 to 176. Suddenly, the Southerners had the balance of power.

In the weeks since the budget victory, the Southerners -- to their own astonishment -- have been the center of Washington's attentions. The White House had wooed them with respectfullness and gusto. The press has built up as the linchpin in the tax-bill fight. And the liberals have paid them court.

But their tactics on the tax-bill fight also may have soured some onetime admirers. For weeks, House Democratic leaders have been making major concessions to the Southerners in an effort to prevent another mass defection, endorsing several Dixie-backed provisions that ordinarily would have been an anathema.

Then, just as the administration and House Democrats were getting close to a compromise, the Southerners pulled out the rug and agreed to go in with the White House on a new "bipartisan consensus" package barley changed from Reagan's original proposal. Democratic leaders were left out on a limb.

Stenholm concedes that the turnabout left the Southerners with "egg on our face. I'd admit publicly it looks as if we didn't bargain in good faith," he says. "That's one thing I regret." Another Southerner puts it more candidly: "We just hurt our credibility," he says.

The preponderance of Dixie legislators in the forum's ranks inevitably has conjured up visions of the Southern bloc of earlier days -- the rigid, often flamboyant group, also nicknamed "Boll Weevils," which regularly teamed with the GOP minority to Block civil rights legislation.

But today's Weevils reject such comparisons -- and with good reason. The mid-'60s Southerners were motivated largely by the race issue; on economic matters, they often were populists, willing to vote with mainstream Democrats on any measure that wasn't linked directly with blacks.

By contrast, Stenholm and his colleagues are economic conservatives. None is known for demagoguing on the race issue. In fact, the 47-member group isn't even solidly Southern. There are two Westerners and one aberrant Yankee -- Rep. Sam Stratton (D-N.Y.), linked because of his interest in more defense spending.

If anything, the modern-day Weevils are closer ideologically to suburban Republicans. Their interest center on three major issues: cutting spending to lower the budget deficit, reducing taxes and increasing overall defense outlays.

Although Stenholm invariably serves as coordinator and chief spokesman, there are other heavies: Gramm, a former economics professor, is the group's intellectual force; Hance serves as front man on tax-cut issues; and Rep. G. V. Montgomery (D-Miss.), who has the largest office, provides meeting-space.

To minimize the danger of public bickering, the forum avoids taking any formal nose-counts on key issues and shuns any regular meeting schedule. However, not all its meetings are sunshine and magnolias. A recent session on the tax cut led to a bitter spate between Gramm and Jenkins.

The Weevils' two-time dalliance with the GOP has brought bitter denunciations from mainsream Democrats, many of whom already view the Southerners as Republicans in Democratic clothing. "A lot of them would be better off just to come clean and switch parties," grouses one senior Democrat.

Forum leaders reject such criticisms as overdone. "There are 15 or 20 in the group that are always going to vote with the Republicans, but the rest are pretty independent," one member insists. And Stenholm notes that in his own case, 16 of the 33 counties in his district went for Carter last November.

Will, then, what is the difference between a conservative Democrat and a Republican? "Fiscally and defensewise, there is very little difference," Stenholm admits. But he's quick to point out that the philosophical agreement won't necessarily spread to all key issues.

Take agriculture for example, muses the former Texas cotton farmer, randomly picking the issue most dear to his constituents' own pocketbooks. "President Reagan is very free-market oriented, and so am I," Stenholm insists. "But there is no such thing as a world free market on agriculture."

Jenkins is somewhat more circumspect about it all. The way he breaks it down is, Republicans flatly oppose all government involvement; mainstream Democrats want more of it; and the Southerners are willing to consider it if the private sector declines to do the job.

Can the Southerners pull off another Gramm-Latta on the tax-cut bill? Most observers say yes. As Gramm himself is fond of pointing out, "we're already a lot farther along than we were at the same point in the budget fight." And the White House is pulling out all the stops. Victory seems close at hand.

However, Stenholm and others are laying it cautiously, noting that the forum itself if "split" between Reagan's three-year tax reduction and the Democratic-sponsored two-year bill. "The budget vote," he says, "was the easiest vote we will cast all year."

But the jury still is out on the longer run question -- how long the new Dixie-GOP coalition will last. Although the Southerners themselves insist that the alliance can go on indefinitely, others predict that the romance will prove a sometime thing.

As one mainstream Democrat sees it, the two sides come from too "different families" to count on a long marriage. "As long as Reagan needs them, they'll be courted," he says. "But eventually the Republicans will want to elect Republicans in their place. And local Democrats will press to defeat them.

Indeed, party discipline already may be tightening. Democratic National Committe Chairman Charles T. Manatt was reported to have told labor leaders on Thursday that he would like to be able to kick Gramm out of the party -- although he hadn't yet found a way to go about it.

And Dixie lawmakers indicated last week that they may well join mainstream Democrats in backing smaller spending cuts than the administration wants on the upcoming "reconciliation" bill. Georgia Rep. Bo Ginn complained publicly that the Southerners were "tired of being manipulated" into backing the GOP position.

To Stenholm, however, it's more than a more alliance at stake. "I think the next few years are going to be crucial in deciding the role of the two parties," he asserts. "Sure, we catch a lot of heck from yellow-dog Democrats. But we're getting a lot of private encouragement from all over the country."

Meanwhile, the Southerners are going for broke in the tax-bill fight, putting aside -- at least for the moment -- any second thoughts about their role in the party. "We're functioning just like we functioned over the last four years -- except right now we're winning," Charlie Stenholm says, grinning.

On Stenholm's desk is a miniature cotton bale -- a memento from a Dawson County, Tex., trade association that apparently appreciates his willingness to remain "independent" on the farm issue. But Charlie Stenholm is true to his word. There's not a single boll weevil in the entire bale.