President Reagan stood his ground yesterday in defense of dividend and interest withholding after a member of the Republican congressional leadership said Reagan would be overridden if he vetoed a bill to scrap the idea.

Rep. Richard L. Cheney (R-Wyo.), chairman of the House Republican Policy Committee, told reporters that the nearly unanimous judgment of GOP leaders on Capitol Hill is that the withholding provision of the 1982 tax bill, scheduled to take effect July 1, "is creating a hell of a problem" for Republicans "and we ought to get off it."

But Reagan told reporters that the complaining citizens were being "misled" by banks and savings and loans, and reiterated his contention that there is no other cost-efficient way to collect the lost revenues.

Cheney said that at a meeting with the president last week everyone in the GOP leadership except Senate Finance Committee Chairman Robert J. Dole (R-Kan.), author of the withholding provision, told Reagan that the issue "was very painful for Republicans."

He quoted an exchange in which Sen. Strom Thurmond (R-S.C.) asked Treasury Secretary Donald T. Regan how many additional Internal Revenue Service agents it would take to collect the additional billions the administration expects to reap from withholding 10 percent of interest and dividend income.

When Regan said he would have to hire 2,000 more agents, Thurmond, according to Cheney, said: "Hire 'em. It's cheaper than losing the next election."

Thurmond confirmed the accuracy of the quotation, but said it was meant as a joking observation.

Cheney said so many members of Congress feel the same way that the House and Senate can override a presidential veto of a repealer bill, if it ever comes to that. A Senate leadership aide said he thought Reagan might prevail in that body, but he acknowledged that it would take a hard fight.

The Wyoming congressman, normally a Reagan loyalist, said the issue was particularly tough for Republicans, in part because "we criticized the hell out of Jimmy Carter when he proposed it" and in part because "a lot of the protests come from our own folks and from senior citizens we already have problems with."

But the president reminded the group that there would be exemptions from withholding for most of the elderly and most families of limited income, and denied that he was seeking another way to end the widely acknowledged tax evasion that he estimated at "$5 billion to $7.5 billion a year."

A Treasury spokesman also said that he was unaware of any search for alternate collection methods, noting that Regan wrote Dole this month that an expanded audit program might cost the government as much as half the additional amount to be collected and would entail a burden of time and paperwork for the audited taxpayers as well.

Dole aides said he was also holding fast, after managing to postpone a vote on the issue until April 15. But reports circulated that his staff was exploring less politically painful options.

The president appeared unyielding in his attitude, however. Rejecting the contentions of Cheney and other Capitol Hill Republican leaders that the issue is becoming a big loser for their party, Reagan said that polls he has seen show voters "more evenly split" on the question.

And a presidential aide said he felt "very strongly the president is on firm political ground in blasting the banks for whipping up public opinion on this issue, instead of lowering interest rates."

He called it "a matter of principle" for the president.