Congressional prospects for the bipartisan Social Security rescue plan were complicated yesterday as two key Democratic leaders urged that a proposed delay in cost-of-living increases in benefits be coupled with a rollback or delay in this year's scheduled tax cuts for upper income groups.

The comments by House Majority Leader James C. Wright Jr. (D-Tex.) and Senate Minority Leader Robert C. Byrd (D-W.Va.) were the first suggestion that Democrats may try to link President Reagan's tax cut program to the Social Security financing agreement worked out by a special commission earlier this month.

They came as the powerful Business Roundtable, composed of chief executive officers of 200 of the nation's largest corporations, endorsed the Social Security plan in large part at the behest of Robert A. Beck, chairman of Prudential Insurance Co. and a member of the commission that drafted the plan.

The agreement includes, along with stepped-up Social Security tax increases and other adjustments, a six-month delay in cost-of-living increases for Social Security benefits that are scheduled to be paid on July 1.

That is also the day that a 10 percent cut in individual income taxes, the third installment of Reagan's tax cut program, is scheduled to go into effect. But, until now, no congressional leader has suggested that the cost-of-living delay and tax cut be linked.

Wright and Byrd emphasized that they were speaking only for themselves, and an aide to House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) said O'Neill, who had joined Reagan in embracing the plan, "does not intend to do anything that would get in the way of making the Social Security System solvent."

However, a Senate Republican leadership aide said the suggestions from Wright and Byrd "put politics back in the Social Security debate" and could pose problems for congressional passage of the Social Security plan if other Democrats line up behind them.

What Wright and Byrd appeared to be doing was using the Social Security plan, with its high-powered backing and sense of urgency, as leverage to force a reduction in what the wealthy would get out of the third year of the Reagan tax cut.

But Reagan adamantly opposes any change in his tax cut program, and other backers of the Social Security compromise have said it is so delicately balanced politically that any tampering could jeopardize its chances of passage.

Byrd's and Wright's comments came separately within a few hours of each other as the 98th Congress returned from a three-week recess after formally convening Jan. 3, and generally marked time while preparing to hear Reagan's State of the Union address.

"I certainly don't want a six-month delay in Social Security while leaving in place the third year of the tax cut . . . for upper-income people," said Byrd in a pre-session talk with reporters.

"It would be grossly unfair and enormously unjust to require these sacrifices of the old . . . and not exact any sacrifice at all from the wealthiest," Wright later told reporters after a meeting of the House Budget Committee.

Wright suggested eliminating the tax cut, deferring it or putting a $700 cap on savings for any individual taxpayer. Byrd suggested phasing out the tax cut for higher income taxpayers and eliminating it entirely for those with incomes exceeding $65,000 a year, a proposal pushed unsuccessfully by Senate Democrats last year.

Wright had previously endorsed the Social Security plan, but Byrd has withheld judgment and did so again yesterday, saying only that "it augurs well that they the commission members were able to get together."

In other developments as Congress prepared to get back to work, Senate Majority Leader Howard H. Baker Jr. (R-Tenn.) said the Senate would begin work on major legislation, including matters left over from the 97th Congress, as soon as possible.