Having carefully built a coalition with Southern Democrats to pass his tax bill, Ronald Reagan suddenly found himself and his program endandered by ferocious business.

Well-paid lobbyists of big business were furious last Thursday when they found the bill's fast tax write-off diminished to make room for sweeteners desired by Congress. In an unpleasant meeting at the Treasury the next morning, the business operatives threatened to withdraw their support and go over to the Democrats unless their demands were met.

"That's just greed," one official muttered after the lobbyists left. Greed or not, President Reagan faces this choice: whether to appease big business at the risk of unbalancing his carefully wrought compromise or to take the right-wing populists' course by defying the corporate boardrooms.

From the start, Reagan has stressed individual tax incentives. Marginal rate cuts, not faster depreciation, is the heart of supply-side incentive for work and production.

Accordingly, it was not difficult for Reagan policy-makers to pare down lavish corporate benefits to accommodate Southern Democratic concern over big budget deficits. That reduction enabled Reagan to push for a 15 percent across-the-board individual rate cut by mid-1982.

It also enabled the administration to put Southern-flavored goodies in the bill -- reduced inheritance taxes and (agreed to at the last moment) exemption of small royalty owners from the oil windfall profits tax.

The last concession to Southerners was made by Reagan himself when some 30 Southern Democratic House members met him at the White House Thursday afternoon. When they wondered aloud about wandering in the political wilderness as men without a party. Reagan made a remarkable promise: no Democratic congressman who supports his program will be opposed for re-election in 1982 by the Republican president. "I couldn't look myself in the mirror if I did," Reagan added.

Rep. Bill Nelson, a conservative Florida Democrat, was ready to announce his backing -- until he received a Thursday night telephone call from the National Federation of Independent Business. The lobbyist urged Nelson to withhold support, at least until the depreciation provisions were worked out.

NFIB's hostile reaction reflected the firestorm among business lobbyists. It was fanned by Rep. James R. Jones of Oklahoma, the astute Democratic chairman of the House Budget Committee, who told business leaders this was their reward for supporting the "crazy" Kemp-Roth tax cuts. "If the administration sticks with this," snarled one Republican lobbyist, "We'll get what we want from Jim Jones."

The fury burst forth in an 11 a.m. Friday metting at the Treasury where Reagan's tax strategists, Treasury Secretary Donald T. Regan and White House Chief of Staff James ybaker III, sat down with the enraged lobbyists. The business operatives were beside themselves because they had not been consulted.

Richard Rahn, chief economists for the U.S. Chamber of Commerce, stormed that "we supported you" on individual tax cuts only to be betrayed. John Post, an executive director of the Business Roundtable, threatened a defection to the Democrats.

"We need your support badly," Baker pleaded. But the administration's tone grew less conciliatory in the face of unrelieved hostility. Don Regan wondered whether big business ought to complain about tax relief worth $24 billion in 1984 in the reduced version when Congress "is voting down food stamps, against the halt the blind and the poor."

Whether big business can really disown Reagan and go to the Democratic window is doubtful. Jones might have touble carrying a majority on the Ways and Means Committee (where Rep. William Brodhead of Michigan, chairman of the liberal Democratic Study Group, has been preparing an onslaught on the bill's depreciation provisions).

Nevertheless, the lobbyists left Friday's sour session at the Treasury convinced Regan and Baker would back down rather than rish losing business support. If so, the president would be passing up a golden chance to show that he was not the first choice of the corporate boardrooms for the White House, does not set policy to suit them and certainly does not now dance to their tune.