Prospects for Senate passage next week of the largest tax hike in peacetime history have increased sharply because several key business groups now support the measure and efforts to mobilize Democratic opposition appear to be faltering.

In addition, some industries directly hurt by the tax bill, including banking, are holding back because the Senate Finance Committee chairman has threatened even more damaging tax measures if any of the existing proposals are killed on the Senate floor.

Although the measure takes back some of the business tax breaks enacted last year, the National Association of Manufacturers has sent a letter to senators supporting the "broad thrust" of the bill, and the American Business Conference has organized a coalition of trade and corporate groups to back the $21 billion proposal.

Even the U.S. Chamber of Commerce, which has been the leader of business opposition to a tax increase of any kind, will not oppose the full bill, seeking instead to win some specific changes. "We're trying to be realistic about what can be done at this time," said Richard Rahn, the organization's chief economist.

Among Senate Democrats, an effort by Russell B. Long (D-La.) to build unified party opposition to the measure in its entirety or support for a major revision of the bill has encountered at best a lukewarm response.

Long has been considering a major revision of the tax bill that would eliminate the July 1, 1983, tax cut of 10 percent for those making more than $40,000 a year. With those additional revenues, Long then would be able to eliminate sections of the bill calling for doubling the cigarette excise tax, adding 10 percent withholding of interest and dividend income, and reducing the deductibility of medical fees.

According to aides, Long believes that solid Democratic support is essential to any successful attack on the bill and, without it, he is unlikely to conduct a formal attack. "Sen. Long is many things, but he is not suicidal," an aide said, noting the Louisiana Democrat's deep aversion to losing on the Senate floor.

Although many business groups are supporting the measure on the Senate floor, and others are signaling that they don't intend to put up a strong fight, the likelihood remains that many of these same organizations will seek significant revision when the House Ways and Means Committee takes up the tax increase next week.

Much of the potential business opposition to the tax bill has been diffused by what amounts to a set of legislative threats by Senate Finance Committee Chairman Robert Dole (R-Kan.).

If elements of the bill are killed on the floor, Dole has a list of his own amendments that would jack up the corporate minimum tax and increase the proposed levies on the insurance and contracting industries.

A spokesman for the American Banking Association, which is opposed to 10 percent withholding on interest and dividend income, indicated that the organization may not try to have the section pulled on the Senate floor because of the possibility that "the next thing you are faced with is the minimum tax . . . There is one scenario that suggests there could be that type of interplay."

A minimum tax set at 15 percent would be a major burden on many banks.