Some of the props that Congress used to balance its budget plans for 1981 collapsed yesterday, prompting warnings that deeper spending cuts will be necessary to keep the country out of the red next year.

Meanwhile, House and Senate budget conferees knocked out funds added earlier by the Senate to assure continuation of Saturday mail deliveries, which the House proposed to end. The action would make it difficult, but not impossible, conferees said, to continue six-day deliveries.

Even before the conferees started trying to reconcile differences in their spending proposals, Senate Budget Committee Chairman Ernest F. Hollings (D-S.C.) brought them the dismal tidings about the budget squeeze.

No longer, he said, could they rely on $10 billion from President Carter's proposed withholding tax on interest and dividends or $900 million in savings from cuts in the food stamp program.

Only a day after a federal judge struck down the oil import fee, a House Ways and Means subcommittee and the Senate Finance Committee voted overwhelmingly to repeal it -- even if it is upheld on appeal. Moreover, Hollings said he had been told authoritatively that there is "no chance" that the withholding proposal will be approved by Congress. And the hoped-for food stamp savings have been eaten up by rising costs, according to Budget Committee aides.

Based on Hollings' assumptions, the Senate's $613.1 billion budget proposal -- hailed as narrowly balanced when it was approved only three days ago -- appeared to be about $1 billion in the red. w

The $611.8 billion House proposal, which was claimed to have a $2 billion surplus when it was adopted earlier this month, would be about $1.4 billion in deficit.

The Senate has dipped into the oil import fee revenues to the tune of about $100 million and had assumed about $900 million in food stamp savings that apparently can no longer be counted on. While the House did not touch the oil import fee revenues, it counted on the $3.4 billion from the withholding tax, which the Senate did not tap.

Despite the bad news, there was no sign that conferees would stop trying to achieve a balanced budget, which has become not only an inflation-fighting weapon but a political imperative for this election year.

"Somehow, by some sleight-of-hand, if necessary, it will be balanced," said one House conferee. Many lawmakers have feared that the recession would throw the budget out of balance by cutting revenues and boosting costs, but assumed that it at least could be adopted before it started to unravel.

While Hollings stopped short of saying the conferees were not dealing with deficit budget proposals, he said it was all the more important to "hold the line" on spending for this year as well as next.

Republicans were less circumspect in their view of the deficit. Sen. William L. Armstrong (R-Colo.), calling the balanced budget a "fantasy," said the proposals are probably about $25 million out of balance right now.

One reason for concern by Hollings and others over the 1980 budget was that both houses had assumed that the oil import fee would produce about $3 billion in revenues this year.

While no attempt was made to balance the budget for fiscal 1980, which is nearly two-thirds over and heavily in the red, loss of the oil import fee would send the current deficit soaring ever higher.

The 1980 deficit was projected a year ago at $23 billion. It had gorwn to $30 billion when the current budget was adopted last November. Now, largely because of spending increases caused by inflation and high interest rates, it is projected at $37.5 billion by the Senate and $42.8 billion by the House.

As of late yesterday, the conferees had tentatively approved spending overruns that would put the deficit more than $1 billion beyond what the House had projected.

Some senators have complained bitterly that, by refusing to cut programs this fiscal year, the conferees are paving the way for more intense spending pressures in 1981. Some of them are defense spending advocates who want to see social programs trimmed to preserve the big military outlay that the Senate approved for 1981. The House approved less for defense than the Senate did.