The House Agriculture Committee, rushing to finish work on a bailout for the financially troubled Farm Credit System, voted yesterday to provide an unspecified amount of federal aid.

After approving the measure, the committee continued to put the finishing touches on its bailout legislation.

The measure approved by the panel on a voice vote would authorize "such sums as may be necessary" to aid the system.

The plan proposed by Rep. Edward R. Madigan (R-Ill.), resolved for the time being at least a debate on the panel over whether to authorize massive borrowing or tap the Treasury for the aid.

An appropriation would be needed to put the measure into effect and the funds are not contained in the budget. It was also clear that the formula could be overhauled either on the House floor or later in a House-Senate conference committee.

"Ain't nobody got any money -- whichever way we go we're going to have to borrow it," Chairman E. (Kika) de la Garza (D-Tex.) told the panel as he kept lawmakers at work late to finish work on the bill. De la Garza told the lawmakers that the House could leave today on its four-week summer recess and thus it was necessary to complete committee action on the measure, which is tentatively set for early September floor debate.

As the panel worked into the night, an initial plan for bailing out the financially troubled, $62 billion system of cooperatives, however, ran into considerable criticism.

Critics urged a counter proposal to appropriate $4 billion to shore up the tottering system, which has lost millions of dollars in recent years because of uncompetitive interest rates.

The plan would authorize the Farm Credit System to borrow $2.4 billion in the bond market using $3 billion in assets it currently holds as collateral. The government would pay the interest over five years at an estimated price tag of $77 million in 1988 and $656 million overall.

If lenders within the system that were buttressed by the bond revenue were unable to service the principal and interest by 1992, the healthier institutions in the network would be assessed under the plan drawn up by Reps. Jerry Huckaby (D-La.) and Richard Nagle (D-Iowa).

Aid to the institutions would be administered by a Temporary Assistance Corp. whose structure already is contained in the legislation.

A number of members expressed doubt that the $3.4 billion in collateral remaining to the Farm Credit System would prove to be substantial enough to make the bonds attractive in the market.

Farm credit officials said the assets consisted of cash, accounts receivable and outstanding loans.

"They're not packaging $3 billion worth of loans and selling them in the market," Rep. Edward R. Madigan (R-Ill.) said. "That's not what's backing these bonds. There ain't nothing backing these bonds."

"I can speak only for the Wichita system," Rep. Pat Roberts (R-Kan.) said, "but we'll be right back here next year" under such a plan.

Huckaby scoffed at the notion that the bond plan would prove too weak a structure to keep the system afloat. "That's the way business is done," he said