Congressional Democrats, in the first round of the new battle of the budget, charged yesterday that Republican proposals to give President Reagan power to impound appropriated funds amounted to "desperation" tactics and a return to the "old ways of Nixon."

As Congress came back to town, frustrated over failure of the financial markets to respond to its early-summer budget and tax cuts, even some Republicans warned of dire consequences if interest rates don't start falling soon. And Republicans seemed somewhat more divided than before.

"Something's got to give" soon or Congress will become "so jittery" it may move toward credit controls, greater regulation of financial institutions and reorganization of the Federal Reserve system, warned House Minority Leader Robert H. Michel (R-Ill.).

In the House, meanwhile, some Republican moderates joined Democrats in opposition to both the administration's plans for additional spending cuts and the impoundment proposals made by their own party leaders. Rep. Bill Green (R-N.Y.) said further cuts in social programs would amount to "a bloodletting and a betrayal" and asserted that Congress would only "pass the buck" if it approved new presidential impoundment powers. Said Green: "I was not elected to be a tail on a dog and I see no reason for Congress to abdicate."

On the Senate side of the Capitol, there was other ominous news. An internal memorandum, prepared late last month by the Republican-controlled Senate Budget Committee, said the Office of Management and Budget's latest deficit "guess" for 1983 was $72.4 billion and for 1984, $78 billion. Even accounting for still-unspecified spending cuts that the administration is expected to propose for those two years, this 1983 projection is $20 billion higher than the highest previous administration estimate, according to congressional budget officials.

Even Republican leaders were not unanimous in support of giving Reagan a limited power to impound, or refuse to spend, money that Congress has already appropriated as one way of helping control federal deficits over the next few years.

Senate Appropriations Committee Chairman Mark O. Hatfield (R-Ore.) was said by an aide to have "serious concerns," and Senate Budget Committee Chairman Pete V. Domenici (R-N.M.) said he questioned whether the impoundment idea would work.

Senate Majority Leader Howard H. Baker Jr. (R-Tenn.), who joined Michel in proposing the idea to Reagan on Tuesday, conceded it will be a "difficult fight" to get Congress to give the president even the limited kind of impoundment authority that he and Michel proposed.

Both House Speaker Thomas P. O'Neill Jr. (D-Mass.) and Senate Minority Leader Robert C. Byrd (D-W.Va.) were critical of the idea, although they stopped short of ruling out any new impoundment authority. Accusing the administration of "really getting desperate," Byrd said Republicans would have to make a "very strong case" for impoundment before Democrats would go along. Said O'Neill: "If they want to go back to the old ways of Nixon, then that's a question for their party to decide."

It was during the Nixon administration that the courts and later Congress curtailed unilateral impoundment of appropriated funds by the president, charging Nixon with abuses of the procedure.

As Michel described the plan, it would be a "fallback" strategy to assure that spending cuts are achieved if Congress fails to keep a sufficiently tight lid on its appropriations bills and a stopgap funding resolution that it must pass to cover money bills that have not been approved by Oct. 1, the start of the new fiscal year.

Impoundment authority would be triggered only if spending exceeded a designated figure, and the president could cut no program by more than 10 percent, Michel said. The authority would last for only one year, and Congress could overrule an impoundment by majority vote of both houses, he added. "I'm not for giving away the whole store," said Michel. He said he hoped the impoundment proposal could be passed as a rider to a debt ceiling extension bill that Congress must pass before Oct. 1.

In other action, the House yesterday rejected, 272 to 122, another attempt to kill the Legal Services Corporation, which provides legal help to the poor. The controversial corporation has been the target of an intense lobbying campaign by conservative groups. It would receive $241 million to operate during the next fiscal year under a $8.8 billion Justice, Commerce and State Department bill approved yeterday by a 246-to-145 vote.