Carter administration officials yesterday told friends, associates and each other that the president's personal campaign to win support for the controversial natural gas bill is working, and some influential lobbyists who oppose the bill said they agreed.

Carter continued to campaign for the decontrol measure yesterday with a plea to representatives of large farm groups and food processors. He again said that defeat of the bill "will have a very damaging effect on our nation."

This so-called national interest argument, which Carter and other administration officials have advanced forcefully in recent days, assisted by Federal Reserve Board Chairman A. William Miller, has evidently had some impact.

"It's working," one gas industry lobbyists who opposes the gas legislation said yesterday. "It's hard to counter."

Administration officials say defeat of the gas bill would demonstrate to the world that America lacks "the national will" to cope with its energy problem, inviting a further run on the dollar and a new blow to American prestige abroad.

Increasingly, administration spokesmen are urging interested parties and members of Congress to pay less attention to the details of the bill than to the implications of failing to pass what Carter now calls the crucial element of his energy program.

(The president used to call his proposed crude oil equalization tax the crucial element of the energy program, but that proposed tax is now considered dead, and the administration's attention has passed to the gas bill.)

This approach infuriates some groups that will be directly affected by the legislation, which would decontrol prices of gas by 1985, create complex new price structures for gas and create additional paperwork for bureaucrats, gas producers and others.

But administration officials claim the national interest argument is working on Capitol Hill, and several who are intimately involved in the fight now privately predict victory after a close fight.

Lobbyists who oppose the bill and sources in the administration and Congress agree that Senate Minority Leader Howard H. Baker Jr. (R-Tenn.) could hold the key to the gas bill's fate. This is a role Baker has played in several important Senate votes during the Carter administration, most visibly in the Panama Canal debate.

At the moment Baker is committed to join and support a filibuster to block the gas bill, but this is a holding pattern. Baker was angered by a compromise apparently reached between Sen. James A. McClure (R-Idaho) and Carter on breeder reactor research that would result in no new spending on the Clinch River breeder reactor in Tennessee. He announced his support for a filibuster after learning of this agreement.

If Baker decides to join opponents of the gas bill, he could bring most of the Senate's 38 Republicans with him - many of whom are already inclined to vote against.

Some Republicans have been talking among themselves about the political repercussions for Carter if he is defeated on the gas bill after making such a large personal investment in it. Several interest parties expressed doubt that the Republicans can resist the temptation of trying to defeat the president, particularly since many prominent Democrats will be working against the gas bill too.

On the other hand, Senate Majority Leader Robert C. Byrd (D-W. Va.) is deeply committed to the gas bill and is working hard for it, according to administration officials. Byrd heard a great deal about energy when he toured European capitals for President Carter earlier this year, and personally promised some foreign leaders to back the president's program fully, these sources said.

Yesterday the American Jewish Committee issued a public endorsement of the gas bill, saying some action on energy was a national necessity after more than 18 months of debate. The president of the 3-million-member American Farm Bureau Federation wrote letters to members of Congress urging them to defeat the gas legislation.