The solid core of special interest and business groups that last year formed a key lobbying block behind the Reagan administration's economic program is beginning to divide and crumble.

The shift parallels the deterioration of congressional support from Republicans and conservative Democrats. Continued high interest rates, the prospect of a $91.5 billion deficit and the failure of the real estate and automobile markets to revive have prompted a number of once-solid Reagan backers in the business community to jump ship.

"It's never been so bad," said James D. (Mike) McKevitt, Washington head of the National Federation of Independent Business, the group that gave critical small business backing to the $750 billion administration tax cut. "They NFIB members are dropping like flies."

Challenging the basic supply-side tenents of the administration, McKevitt said, "We are just plain old-fashioned. We don't buy those theories." Supply-side theory was used to justify massive tax cuts which were to have revitalized the economy and produced enough revenue to more than finance the sharp increase in defense spending.

McKevitt is unwilling to declare the Reagan program a failure, but his reticence is not shared by trade organizations representing business groups facing the severest hardships in the current recession.

"We are disenchanted with it," Fred Napolitano, president of the National Association of Home Builders, said about the Reagan program. "Our members have said 'enough is enough.' " A spokesman for the group said, "Our production in 1981 was the lowest since 1946. Our market has been killed."

Last year the homebuilders gave full backing to the Reagan budget cuts and partial backing to the tax cut after the provision establishing "All-Savers certificates" targeted for mortgages was added to the legislation.

Similarly, the National Association of Realtors last year pulled out the stops for the budget cuts, as the organization lobbied members of the House before key floor votes, and backed the administration's tax bill over the Democratic version.

This year, however, the organization has decided that the tax cut is a major factor behind the deficit--and consequently high interest rates, according to the realtors--and the group may use a vote in favor of the legislation as a negative factor when considering whether to support or oppose candidates in the 1982 election.

The growing dissatisfaction within the business community yesterday prompted Senate Budget Committee Chairman Pete V. Domenici (R-N.M.) to say: "Those who are out there in the business world ought to talk more frankly to the president. I don't think he's hearing the same thing from the business community as we are."

Domenici is backing a major revision of the Reagan program that would result in significantly smaller deficits in 1984.

On the other side of the coin, the failure of the business community to respond to the major tax cut and the suggestion by some business leaders that the individual--not the business--tax cuts be postponed, has produced some anger in Congress.

Sen. William V. Roth Jr. (R-Del.), a key sponsor of the individual cuts, described the business community as "a bunch of crybabies. . . . Business is a little like a hitchhiker and now that they are in the car they want to steal it."

The dissention within the business community is by no means unanimous, and those who have become disenchanted do not have consistent responses. Almost all of the groups would like to see cuts made in basic entitlement programs, including Social Security. But, for example, the Business Roundtable would reduce the rate of defense increases, possibly increase excise taxes and, if necessary to reduce the deficit, postpone the individual rate cuts scheduled for 1983.

The NFIB, according to McKevitt, shares some doubts about defense spending but views the individual rate cuts as one of the major benefits going to small businessmen.

Two major business organizations, the Chamber of Commerce and the National Association of Manufacturers, are remaining relatively firmly in the Reagan camp.