White House counselor Edwin Meese III said yesterday that he believes "the progressive income tax is immoral" and that the Reagan administration will resist efforts to cap next year's tax cut for people in the upper income brackets.

"I don't think we should penalize someone because he's successful," Meese said.

In a breakfast meeting with reporters, Meese said that he personally favors a single flat tax rate for all individuals, as opposed to a progressive tax in which rates rise with income. He also said the administration has no plans to overhaul the existing graduated income tax structure, but added, "We're not going to make it more progressive."

The issue was raised in the abortive efforts last month of the White House and House Democratic leaders to reach a bipartisan compromise on reduction of next year's likely federal budget deficit.

House Majority Leader James C. Wright Jr. (D-Tex.) said he had suggested to President Reagan that one way of doing this might be to cap next year's scheduled tax cut at $700, which would mean curtailed tax cuts for individuals with incomes over $45,000.

Wright said Reagan told him: "Jim, that simply compounds the progressivity of our income tax and that's what's got us into all the trouble."

At the breakfast meeting yesterday, Meese continued the vigorous White House campaign of denying that the administration has plans to curb the growth in basic Social Security benefits and attempted to tag Democratic leaders as the ones first proposing such cuts in the negotiations that collapsed last month.

Asked to explain how the White House would achieve the $40 billion in Social Security retrenchment called for over the next three years in the new budget compromise between the administration and Senate Republican leaders, Meese said those decisions would be deferred until the White House receives recommendations of a bipartisan presidential commission on Social Security, which is to issue its report after the November elections.

Meese indicated that he believed the budget log jam on Capitol Hill had been broken by the deal struck with the Senate Republicans. The agreement will provide a "good framework" for negotiations in the House, although Meese said he believed it was "entirely possible" that there may have to be some further changes to get a budget through.

"What we put together with the Senate is pretty close to a final figure of what you're going to get in the Congress," he said.

Meese said Reagan has already talked to a few Democrats "in a sporadic way" in an effort to build a majority coalition in the House similar to the alliance of Republicans and conservative Democrats that supported the president on the budget and tax cut last year.

"You may lose a few Republicans and get a few Democrats," he said. He declined to say where he thought the new Democratic support would come from.

Once a budget is enacted, Meese said, that would serve as a signal to financial markets and catalyst for economic recovery that would lead to lower interest rates by July and continue to drive the inflation rate downward, although he declined to predict by how much he expected them to drop.

High rates of unemployment, which rose to 9.4 percent nationally last month, their highest levels since the Great Depression, would probably hurt Republicans running for reelection, Meese acknowledged, but he said he believed veteran Democrats would suffer too as voters blame economic problems on all incumbents.