Gov. Edmund G. (Jerry) Brown Jr., the slick political gun from the West, met his match in a duel over his balanced budget amendment yesterday.

His quick shooting opponent wasn't President Carter, or any other big political gun from Washington. It was a plain-talking Yankee businessman, Vermont Gov. Richard Snelling, who made no secret of his distaste for the California governor's razzle-dazzle tactics.

When Brown made an impassioned plea for other governors at the National Governors' Association meeting to jump aboard his balanced budget amendment bandwagon, saying it was the "central issue of our time," Snelling cut him short.

He curtly reminded Brown that he hadn't done his homework, or participated in a governors' committee of which he is a member studying proposals to balance the federal budget. Brown also, he said, had not answered a letter he spent to all governors asking them to detail specific federal programs they felt could be eliminated to reduce federal spending.

"We'd very much welcome the contributions of the state of California to that process," Snelling said coldly.

When Brown started talking about the message that California's Proposition 13 sent to the nation last June, Snelling again stopped him. The governors of many states, including Vermont, he said, had acted to cut taxes before voters had crammed tax cuts down their throats.

Later, Snelling, a Republican, said he had decided to get tough with Brown, who harbors ambitions for the 1980 Democratic presidential nomination, because he resented Brown's grand-standing. Brown, he said, was absent "when the hard work of making government is done."

"I think the born-again lines he uses are reasonably offensive to those of us who have worked to reduce taxes for years," Snelling added.

The confrontation occurred during a debate over a resolution governors approved twice last year, calling for the federal government to balance its budget by 1981.

Brown has called on Congress to initiate a constitutional amendment requiring a balanced budget. If Congress fails to act, he has said states should demand a constitutional convention.

Brown, however, didn't ask a governors' committee, headed by Snelling, to endorse the amendment idea yesterday, apparently realizing it would not win approval. Instead, he pushed for the creation of a new committee to evaluate the implications of an amendment.

But Snelling headed that move off before it came to a vote. This left Brown and four allies on the question with only a narrow 5-to-4 victory on a minor amendment, calling for study of state budget balancing efforts.

Brown, however, was unshaken. Faced with defeat, he declared victory. "Today marks the beginning of a national debate on this issue," he said. The fact that the nation's governors had spent much of the day talking about the issue was in itself significant, he added. "Governors usually come here [to Washington] to get more money."

At the end of his committee meeting, Snelling invited Brown to join him for a meeting with Sen. Edmund S. Muskie, chairman of the Senate Budget Committee.

"We'll have an interesting discussion in the cab," Snelling said.

"I think I'll walk," replied Brown.