Despite President Carter's statement yesterday that the "overwhelming majority" of major corporations have promised to comply with his anti-inflation program, there is little hard evidence to back up his claim.

White House officials, when asked who's committed to the program, point to letters from the chief executives of 207 corporations pledging compliance with the price standards, plus a smattering of recently negotiated labor contracts that have fallen within the President's 7 percent wage guideline.

But just as many companies and unions have raised questions and withheld full support of Carter's program as have endorsed it.

And while many in Congress continue to be skeptical about the effectiveness of the program, there were indications yesterday that the administration's chief inflation fighters were also having nagging doubts about the success of their efforts.

Alfred Kahn, chairman of the Council on Wage and Price Stability, stated that the administration's projections for inflation at 7.4 percent for 1979 are likely to be on the "downside." He told the Women's National Democratic Club that it is difficult to expect labor unions to negotiate contracts within the 7 percent wage guideline when the administration itself expects inflation to be more than that.

Kahn's remark followed a government report last Friday that wholesale prices leaped 1.3 percent in January, among the largest jumps in months. Yesterday Kahn termed the increase troublesome but not despairing.

In related news, Alan Lee, a spokesman for the Amalgamated Meat Cutters union, said his group will ignore Carter's wage guidelines in its labor talks later this year. The meatcutters are planning to merge with the Retail Clerks International Association in a move that will make the merged union the largest in the AFL-CIO.

Adding to the legal quarrel that has sprung up around Carter's program, Rep. Benjamin Rosenthal (D-N.Y.) released a Library of Congress report that challenges the president's authority to deny government contracts to companies that do not comply with the guidelines. The General Accounting Office has taken a similar position, contrary to the view of the Justice Department which claims Carter has such authority. The issue is likely to be settled in the courts.

Administration officials say there is still some uncertainty over which major companies will comply with the anti-inflation standards because of the long and confusing process involved in establishing the program during the past three and a half months.

The corporate pledge letters the White House has received came in weeks ago in response to a letter from Carter to the Fortune 500 companies asking for a commitment to his program. Over 400 chief executives responded, but in many cases it was difficult to tell just what a company president was pledging. Many pledged partial compliance or compliance conditional upon clarification of a long list of questions and concerns about the program as initially outlined. The wage-price council staff classified 207 of the letters as "generally positive and supportive" of the president's price standard.

In the period since, the guidelines have been revised and clarified and a variety of special standards for certain industries have been issued. Having answered many of the questions put to it, the council has sent another letter to the 293 holdouts asking if they are now ready to comply.

As a result of the widespread and frequent number of contacts council staffers have had with corporations seeking to understand how the wageprice guidelines apply to their specific cases, the White House expects to receive explicit promises of compliance from most of the country's largest corporations.

"What the president said today is based on sound intelligence." said Joseph Carter, a council spokesman. "We don't think he overstated the situation."