The Senate, heeding Republican leadership warnings against amendments to broaden the measure, passed legislation last night that could lead to last-resort federal financial assistance for the Farm Credit System (FCS), the nation's largest agricultural lender.

The final vote was 57 to 34.

The "fast track" bill, sent to the floor without hearings or debate by the Agriculture Committee, would require major management changes in the FCS and give the federal Farm Credit Administration (FCA) more power to regulate the system.

Despite misgivings of the Reagan administration, the measure would pave the way to open-ended federal aid for the FCS if the structural changes fail to shore up the system.

Similar legislation is moving through the House Agriculture Committee as part of a congressional effort to enact a bill before year's end and bolster investor confidence in the farmer-owned network of more than 700 banks and associations.

Senate Majority Leader Robert J. Dole (R-Kan.) warned repeatedly that he would pull the bill from the floor if any of the major proposed changes were made in the measure, which was drafted largely by FCS officials.

Dole's admonitions were seconded by Sen. Jake Garn (R-Utah), chairman of the Banking Committee, who deplored the procedures that brought the bill to the floor without hearings as "law of the jungle and every man for himself."

A key feature of the legislation, cosponsored by Agriculture Chairman Jesse Helms (R-N.C.) and Edward Zorinsky (D-Neb.), would allow the FCS to move assets around the system more quickly in order to prop up its weaker segments.

Helms and Zorinsky justified the unusual no-hearings procedure on the ground that the FCS and FCA need urgent help to reassure investors and to avoid new interest-rate increases for farm borrowers.

Zorinsky agreed with critics that mismanagement has plagued some parts of the huge FCS, which holds about a third of the nation's $214 billion farm debt. But he said it is "essential that Congress provide legislative remedies as soon as possible."

Rapidly declining land values, particularly in the Midwest grain belt, and the prospect of continued low prices and weak exports have eroded the FCS loan portfolio and pushed thousands of farmer members closer to bankruptcy.

These developments in turn have made investors nervous and affected the system's ability to raise money in the bond market at its traditionally favorable rates. As a result, many of the FCS banks and lending associations have raised interest rates on loans to farmers.

Amendments rejected yesterday included:

*One by Sen. Max Baucus (D-Mont.) to put more control over the FCS at the local level. Baucus charged the bill would create a "megabank" in the form of an FCS capital corporation that would manage the system's assets.

*Another by Sen. Rudy Boschwitz (R-Minn.), who wanted federal aid for commercial banks and insurance companies involved in farm lending. Boschwitz said his proposal would have cost $1 billion annually for three years.

*A move by Sen. Patrick J. Leahy (D-Vt.) to limit the amount of funds the capital corporation could shift from the FCS' more solvents banks to trouble spots.

*A proposal by Sen. Tom Harkin (D-Iowa) to require the corporation to give priority to the original borrower when it proposes to sell or lease land from its inventory.