RICHMOND, JAN. 26 -- Virginia Lt. Gov. L. Douglas Wilder, challenging Gov. Gerald L. Baliles' contention that there is no room in the state's proposed $22.5 billion budget for a tax cut, urged the Senate Finance Committee today to support a bill that would eliminate the sales tax on nonprescription drugs.

"I can't imagine anyone at all who would not want to remove a tax that is regressive," said Wilder, adding that proposal would relieve the tax places an unfair burden on the aged, poor and chronically ill.

The legislation would exempt over-the-counter remedies, such as those that combat headaches, colds and sore throats, from the 4.5 percent sales tax. State budget analysts estimate it would cost the state $60 million in the biennium that begins July 1.

If adopted, Wilder's proposal could become a keystone of his expected campaign for governor next year.

"We ought not to forget that Virginia enjoys a record budget surplus," which is "a consequence of both tax reform and economic growth," Wilder said. "The surplus resulting from tax reform is due the taxpayers.

"There is no reason to believe that a repeal of this tax would raise the ugly specter of cuts in essential programs, within the present $22.5 billion budget or any future budgets," he added.

The governor's press secretary, Chris Bridge, said that while Baliles is "not supporting it {the Wilder tax cut}, he is not out to defeat it either." She noted that the governor's proposed budget includes "no tax increases and no reductions. Wilder has not identified where he would get the money" to offset the loss in revenue.

Taking note of the state's healthy economy, Wilder told the Finance Committee, "I'm not disparaging our good fortune, but the elderly on fixed incomes and the unemployed and working poor . . . unless they read about it in a newspaper, would never know . . . about the commonwealth's good fortune, for they certainly are not experiencing it first hand."

Sen. Dudley J. (Buzz) Emick Jr. (D-Botetourt), who introduced the legislation in Wilder's behalf, said, "The mood is to give some degree of tax relief."

Two other tax-cutting proposals were heard by the Finance Committee today.

Sen. J. Granger Macfarlane (D-Roanoke) has proposed legislation similar to Wilder's, except the tax break would be limited to persons 65 and older. His plan would cost about $28 million over the next two years.

Sen. Clive L. DuVal 2d (D-McLean) wants to give a $3,000 income tax deduction, minus Social Security benefits, to retirees. The bill would primarily benefit former federal workers, because most nonfederal retirees already get more than $3,000 from Social Security benefits. DuVal's bill, which has been rejected in past years, would cost between $7.2 million and $8.8 million in the 1988-90 budget.

Oscar J. Honeycutt, vice president of the Virginia chapters of the National Association of Retired Federal Employees, said it would provide a maximum of $172.50 a year in tax savings to about 31,000 residents.

A number of states give deductions to civil service retirees, including Maryland, which exempts $9,100 of income, Honeycutt said.