President Reagan's new "bipartisan" tax-cut plan ran into a cross fire yesterday when business threatened to bolt over a reduction in its share of relief and critics in Congress said the president may have set off a "bidding war" with Democrats.

In a meeting with Reagan aides, spokesman for a dozen big business groups losing business support if it did not return to the president's original plan for increasing depreciation write-offs.

Meanwhile, House Ways and Means Committee Chairman Dan Rostenkowski (D-Ill.) comlained directly to Reagan that the administration had reneged on a promise to continue compromise efforts when it moved to draft a coalition bill with Republicans and conservative Democrats.

"Procedurally, we're at opposite ends of the globe -- and we're going to be at war about that," Rostenkowski said he told the president in a telephone conversation yesterday morning.

He accused the administration of "auctioning" off parts of its bill by sweetening pet tax-cut proposals, such as one that would ease oil taxes for royalty holders, in exchange for the votes of individual senators and congressmen.

On Thursday, Reagan came out with a revised proposal for rate cuts of 25 percent spread over three years plus an assortment of additional cuts for married couples, people with interest and other investment income and other specific groups.

The Democrats also favor many of these specific proposals, but want only a two-year, 15 percent cut in rates. They say Reagan's proposal would be inflationary.

Yesterday's churning set the stage for a possible "bidding war" when the tax-writing committes begin markup next week -- with Republicans and mainstream Democrats vying to outdo each other to attract support.

Rep. Barber B. Conable Jr. (N.Y.), ranking Republican on the Ways and Means panel and cosponsor of Reagan's new plan in the House, said he expects the two sides "to get into a bidding contest," particularly over the business tax cut.

And Rostenkowski raised the same possibility, noting that the business tax reductions outlined by Ways and Means Democrats last week already are larger than Reagan's revised proposals.

"I haven't changed my mind on those," he said.

The president's latest revisions have drawn a backlash from business. To save money, Reagan cut his depreciation plan to give firms 30 percent less in write-offs than previously intended. And his change-of-mind came as a surprise.

Sources said business spokesmen at yesterday's meeting warned that the White House must restore at least part of the cutback in tax breaks if it is to hold industry's support for its tax-cut package.

However, administration strategists said they doubted the president would change his mind, in part because White House strategists believe they must trim the tax package and lower the budget deficits projected over the next three years to attract conservative support.

Top administration planners are expected to give the business community an answer early on Monday, in time for a previously scheduled meeting of the Business Roundtable, an organization of larger corporations, that night.

Treasury Secretary Donald T. Regan, who met with the business groups yesterday morning, told reporters later that the tax fight is "going to be difficult, but we do think we are going to win it."

The Ways and Means Committee is scheduled to begin markup of the tax package next Wednesday, and the Senate Finance Committee will start work the same day.

Meanwhile, both sides stepped up their efforts to repeat, or prevent, another defection by southern Democrats similar to the one that gave Reagan his overwhelming budget victory last month.

The White House confirmed yesterday that the president had promised conservatives that he would not campaign against them in 1982 if they defected to support his key legislative programs.

At the same time, some liberal Democrats suggested the party punish defecting conservatives by assigning them to less-desirable congressional committees -- perhaps at the judgment of the Democratic caucus.

Several key Democratic House members accused their conservative colleagues of stabbing the party's leadership in the back by joining Reagan's new tax-cut coalition. They also complained the president had abandoned compromise efforts.

The liberals, however, appeared unable to muster steam for a serious protest.