When President Reagan vetoed the Treasury and Post Office appropriations bill last month, the Internal Revenue Service was among the victims. It was nicked unintentionally in this latest skirmish in the budget wars. The case of the IRS illustrates the truth that not all budget cuts save money.

The chief reason for the veto was a quarrel between the president and Congress over postal subsidies. But the money for the IRS was in the same bill. The administration had originally wanted to cut the 1986 support for the IRS. Then the delays in processing income tax returns last spring, and the late payment of refunds, generated a chorus of complaints and drew attention to the agency's troubles in handling a rising tide of paper with decreasing resources. Instead of reducing the budget for the IRS, Congress voted to increase it slightly.

It's one budget increase that is no longer at issue. The White House heard the public complaints just as clearly as Congress did, and on second thought decided that a modest increase would be a good idea after all. If the Treasury appropriation is not enacted this year, the administration says, it intends to ask for a supplemental for the IRS in January. But this help for the agency will have been delayed, in effect, for another tax year.

Congress and the administration are both well aware that slow processing of returns, and public irritation, are only a small part of the cost of an understaffed tax collection agency. When the House Budget Committee last spring recommended another $42 million a year for tax enforcement, it calculated that the additional examiners would raise more than $350 million a year in taxes that would have remained uncollected. That's a ratio of more than $8 in revenue collected for every dollar spent checking returns. The Senate, in the reconciliation bill that it passed several weeks ago, suggested that the ratio might be even higher.

In the budget resolution that it passed last summer, Congress cited an IRS estimate that the tax enforcement gap is currently running about $92 billion a year. The resolution declared congressional support for "increased and improved enforcement and collection, through audits, examinations and other steps designed to identify and eliminate tax cheating . . ."

There are many points in the budget at which across-the-board cuts result not in greater efficiency but the opposite. The IRS is an unusually clear example because its limitations can be measured directly in revenues not paid and deficits that, even under present tax law, are larger than they ought to be.