Supporters of a constitutional amendment mandating a balanced federal budget ran into a strong streak of skepticism yesterday among the people they most need to convince -- state legislators.

Among some 200 legislators from around the nation here for an assembly of the National Conference of State Legislators, expressions of doubt or outright opposition to the amendment proposal seemed as common and as fervent as speeches in support of the balanced-budget drive.

At the assembly's closing session, legislators who want to convene a constitutional convention to propose such an amendment failed to win approval of a mild resolution on the subject.

The assembly's reaction made it clear that the constitutional convention drive, a movement that a few weeks ago seemed to be gliding along with almost no resistance, has run into much tougher going now that opponents are fighting back.

A constitutional amendment can be proposed either by Congress or by a convention called at the request of two-thirds of the states. In either case, any proposed amendment would have to be approved by three-fourths of the states.

Supporters of a constitutional amendment on the budget, believing that Congress would not take the initiative, have been campaigning in the state legislatures to cosnvince the necessary 34 states to call for a convention to propose the amendment.

Leaders of the campaign say 28 states have already asked Congress to convene a constitutional convention. Some of the state resolutions, however, would not require Congress to do so immediately.

The constitutional convention campaign was a prime topic at the assembly here. The legislature heard presentations from James Davidson, the president of the National Taxpayers' Union, the lobby group that is coordinating the campaign, and from Sen. Edmund Muskie (D-Maine) and California House Speaker Leo McCarthy, both strong critics of the idea.

And legislators lobbied one another at every opportunity. Jason Boe, president of the Oregon Senate, worked hard to convince his colleagues from states that have not passed convention calls to join the bandwagon.

But Boe met considerable resistance, particularly from legislators in the Northeast, where the convention drive has fared poorly so far.

"The whole idea sounds dangerous to me," said Barry Hobbins, a Maine legislator, in a corridor confrontation with Boe. "This convention idea -- who knows what would happen? And a balanced budget just won't work."

Boe replied that a convention is needed because Congress has been unresponsive to the public's demand for limits on taxes and governmental spending.

However, Boe decided yesterday not to propose a formal resolution calling for a balanced budget amendment, because he was not sure he could garner the votes needed to pass it.

Instead, he proposed a seemingly innocuous resolution asking Congress to establish procedures for a constitutional convention in case one is called. That resolution was also attacked by opponents of the balanced budget idea, who said its passage might indicate that the legislators' conference favors calling a convention.

The resolution was backed by a majority of the 28 states represented, but fell short of the three-quarters' support needed for adoption.

The legislators also defeated, by a large margin, a resolution asking Congress to eliminate the nationwide requirement for a 55-mile-per-hour speed limit. The speed limit was attacked angrily by legislators from the West, but was supported by delegates from other regions.