The banking industry has nearly enough support in Congress to repeal a new law requiring withholding of dividend and interest income, according to the industry's House and Senate supporters.

In a face-to-face confrontation with bankers here yesterday, Senate Finance Committee Chairman Robert J. Dole (R-Kan.) accused them of waging a dishonest campaign to convince Congress to repeal the withholding requirement, scheduled to go into effect July 1.

Dole threatened the industry with reprisals as he sought to head off the repeal movement, which now has the support of a majority of the House and a near-majority in the Senate. He said he has urged President Reagan to announce that he would veto any bill that strikes down the withholding provision, even if it is Social Security legislation or unemployment aid.

The banking industry has waged a massive, expensive effort to convince depositors that the withholding will cost them money and should be repealed.

The American Bankers Association, for example, has provided speeches, postcards, flyers and other materials to the nation's 14,000 banks. One prepared speech claims that Congress has "looted" savings accounts. An advertisement alleges that 10 percent of interest earnings will "disappear."

Congress has been deluged with mail on the issue, much of it on postcards provided to depositors by their bankers. Sen. Robert W. Kasten Jr. (R-Wis.), who is spearheading the repeal fight in the Senate, said the amount of mail the bankers have generated is a record by any standard he knows.

Dole told a meeting of the ABA leadership that the Finance Committee will hold hearings March 11 "to review some of the special tax preferences enjoyed by various members of the financial services industry including banks, credit unions, and savings and loans."

If withholding is repealed, he said, Congress would have to find some way to replace the $20 billion lost to the Treasury between 1983 and 1988.

The law does not provide for any new taxes on income received from dividends or interest payments, but tries to stop taxpayers who cheat. It requires institutions to withhold 10 percent of dividend and interest payments, much as employers are required to withhold income taxes on wages and salaries.

"What's so wrong with asking people to pay their taxes?" Dole demanded to know.

Dole insisted that the repeal movement would fail. However, 47 senators have co-sponsored repeal legislation. Kasten said nine co-sponsors were Republicans who originally supported the withholding provision in last summer's tax bill, when it survived by a 48-to-47 vote.

In the House, 230 legislators have co-sponsored a repeal bill, far more than the 218 majority needed. But because of the House rules, it will be far more difficult than in the Senate to have a floor vote on repeal.

If, as Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) has indicated, the House Democratic leadership actively opposes repeal, then sponsors will be forced to get 218 signatures on a discharge petition to force a vote. Members are more reluctant to challenge the leadership by signing a discharge petition than they are to simply co-sponsor legislation.

Dole told the bankers' group that banks should not hesitate to speak out on issues of concern, but "should do so accurately and responsibly, precisely because of the trust so many Americans place in their banks and bankers."

"Unfortunately, the campaign to repeal withholding has hardly lived up to that standard. From my perspective, the tactics used by many banks, savings and loans and credit unions have reached an historic low," he told the bankers.

Dole said they have made a "great deal of noise" about the money that savers will lose if 10 percent of their interest is deducted from their accounts and is not compounded. He said that on a $1,000 deposit earning 9 percent a year the loss is less than 50 cents. And if banks choose to withhold only at the end of the year, as they are permitted to, there would be no loss of compounded interest.

He said that if banks are truly concerned with consumer issues they might push for faster de-regulation of passbook accounts. Because the new money market accounts require a $2,500 minimum deposit, an individual with only $1,000 to put in a bank loses $25 a year. The 50-cent loss because of withholding is "trivial" contrasted to that, he said.

David Hastings, senior vice president of Richmond's First & Merchants Bank who is heading the fight for repeal of withholding, said the banks will continue their lobbying effort.