The House and Senate, reluctant to confront the tax increases required by the fiscal 1984 budget resolution they passed just last month, agreed earlier this week to a two-month delay in the budget's mandate for drafting legislation to raise taxes by $73 billion over the next three years.

Congressional budget aides said it was the first time that such a delay had been necessary since Congress began using the budget to force revisions in tax and spending laws four years ago.

The budget, approved June 23 over strong objections from President Reagan, called on the tax-writing committees of both the House and the Senate to prepare a three-year tax bill by yesterday.

But, when the leaders of the Senate Finance and House Ways and Means committees complained that they couldn't muster support for major tax legislation without support from the White House, the two chambers agreed Thursday to delay the deadline until Sept. 23 in hopes that the impasse could be worked out in the meantime.

"The White House has to send some kind of a signal if we're going to get it done," said an aide to the Senate Republican leadership.

The congressional budget resolution proposed tax increases of $12 billion during the 1984 fiscal year to start Oct. 1, $15 billion in fiscal 1985 and $46 billion in fiscal 1986, all of which were to be imposed in legislation that Congress would enact by later this summer.

The Reagan administration supports only minimal tax increases over the next two fiscal years and, according to congressional sources, has been sending mixed signals about support for its earlier proposal for about $50 billion a year in stand-by tax increases starting in fiscal 1986.

This creates a political dilemma for congressional tax writers because the Republicans don't want to defy Reagan, the Democrats don't want to be alone in leading the charge for tax increases, and neither party on Capitol Hill wants to give Reagan ammunition for running against Congress in his expected 1984 presidential reelection campaign.

The tax stalemate also affects the congressional budget resolution's proposed $12.3 billion in spending savings through fiscal 1986, which is expected to come largely from Medicare, federal disaster loans and cost-of-living increases for federal pensions.

Although most congressional committees were ready to go with the spending cuts, except for Medicare, they too are being held up because of political pressures, especially among Democrats, to combine any spending reductions with tax increases.