Despite some last-minute flinching by the Senate, Congress appears to have gotten fiscal religion in exorcising the deficit demon from its spending plans -- holding out hope of salvation and maybe even a tax cut.

Prudent taxpayers will not hold their breath waiting for a check from the Treasury Department. But they can draw comfort from watching Congress, forced by political inperatives to get serious about enforcing its six-year-old spending discipline rules, share in their checkbook-balancing miseries.

The Senate underscored the difficulty of keeping the budget in balance last night as it approved politically alluring proposals to save Saturday mail deliveries and add more money for veterans' benefits. But, at the same time, it committed itself to try to live by the spending targets it imposed on itself under the 1974 Budget Control Act, regardless of the difficulty.

In previous years, the first budget resolution has set only tentative goals, subject to revision -- upward, of course -- in a binding resolution just before the fiscal year starts Oct. 1.

This year, under new rules adopted last week by the House and approved by the Senate last night, spending that exceeds initial estimates is supposed to be blocked until compensating cuts are made or until a second resolution is adopted in the late summer or fall.

In a further move to keep spending within predetermined limits, the House voted to direct congressional committees to cut existing programs by $9 million and raise taxes by $4.5 billion.

The Senate has called for savings of $9.6 billion in 1981, along with $2.6 billion for the remaining five months of 1980.

Differences between the two versions will have to be ironed out in a House-Senate conference, which is scheduled to begin today.

Mandated cuts, called "reconciliation" in the budget law, have been only rarely attempted in the past and never before as early as the first budget resolution -- or for as much money.

While there are escape hatches, they would require a politically embarrassing concession by both houses -- in an unusually volatile election year -- that Congress is willfully busting its own budget for a specific need or special interest.

Living with the budget law in earlier years was relatively easy. Targets were generally set high enough to accommodate most swings in the economy as well as most of the spending Congress wanted to do, with a deficit always available to absorb the excess.

But this year, both the Carter administration and Congress, bedeviled by inflation and a widespread public belief that government deficit-spending fuels it, have taken the pledge to produce a balanced budget of just over $610 billion, and about $40 billion above current spending, during 1981.

Never mind that recession could destroy the fragile anticipated balance by eroding revenues and increasing welfare-related costs, meaning the demon of deficits will remain around a while longer.

The political realilty is that Congress is setting itself up to be judged on whether its deeds match its words, at least within the context of forces it can control at the moment.

Cynics are quick to point out that Congress is more zealous in imposing self-disciplining reforms than living up to them, and the budget process appeared earlier this year to be giving them a new arguing point.

Congress knowingly busted through its own ceilings for veterans' benefits and other politically rewarding programs, eventually having to freeze all spending bills after its overall ceiling was breached by inflation-fueled cost overruns.

Moreover, widely heralded efforts to achieve $2.7 billion in voluntary legislative savings eventually yielded only about $200 million, according to advocates of the now-repudiated voluntary approach.

As a result of the failure of voluntary efforts, along with the vise by recession-era spending pressures and political demands for a balanced budget without more tax increases, even some of those who previously shied away from harsh discipline are now embracing it.

Leading the charge in the House was Budget Committee Chairman Robert N. Giaimo (D-Conn.), who only six months ago won out over then-Senate Budget Committee Chairman Edmund S. Muskie (D-Maine), a mandated-cut champion, in giving voluntarism one more try.

"The depth of the conversion is remarkable," marveled Rep. Henry J. Hyde (R-Ill.). "And I say redemption is at hand," intoned Rep. Robert E. Bauman (R-Md.) in amen-revival style. Giaimo grinned and nodded.

None of this or even the lure of what Muskie called a "good behavior" tax cut if the budget stays in balance -- assures that the budget process will survive what is surely its most critical test. In fact, the process may be more fragile now than before because the load it carries is so heavy -- and so much public attention will be focused on every creak and groan.

One early warning sign came as the Senate, in an unsuccessful attempt to finish its budget drafting job last Thursday night, wrote a specific escape clause into its budget resolution. It would allow Congress, by majority vote, to waive temporary freezes on tax or spending bills that exceed budget targets. Although this had reportedly been the intent of the Senate Budget Committee, some influential committee chairmen wanted it nailed down in the resolution, indicating its possible use may be more than just hypothetical.

Reconciliation is also uncharted territory. Over the objection of many of their chairmen, at least in the House, numerous committees would be required in about a month to report legislation that cuts programs by specific dollar amounts prescribed in the resolutions. It is unclear what happens if the committees don't oblige. Rep. James C. Corman (D-Calif.), a high-ranking member of the Ways and Means Committee, which is required to come up with $4.5 billion in revenues, warned that it might take a formal discharge petition to get a tax increase out of the committee.

There is also doubt about congressional willingness to let the government withhold income taxes on savings and dividend income, a $3.4 billion presidential proposal upon which the shaky congressional budget balance is based. There are also efforts to block Carter's oil import fee which Congress is eyeing for a $10 billion "good behavior" tax cut.