The House, panicked by suggestions that it might be making possible a back-door pay raise for Congress in an election year, balked yesterday at a $13.7 billion package of spending cuts and sent it back to House-Senate conferees for overnight surgery.

The conferees immediately scrambled to obtain agreement to delete the offending language, under which members of Congress could wind up with a pay raise by the end of the year without ever voting on it.

An aide to the conferees said enough signatures were in hand by early evening to get the budget-cutting measure back on track for passage today.

Congressional leaders agreed that yesterday's House rejection of the measure reflected skittishness over the pay raise issue rather than opposition to main elements of the bill, which include limits on federal workers' pensions, food-stamp cuts, a two-year dairy price-support freeze and an acreage set-aside program for wheat and other grains.

"Just the rumor of a pay raise is about as popular as an illegitimate child at a family reunion," said Deputy Majority Whip William V. (Bill) Alexander Jr. (D-Ark.).

But the surprise House vote of 266 to 145 against passage of the bill sent a shudder through the ranks of Republicans and Democrats who are pushing for quick passage of the spending cuts to win votes of conservative congressmen for the Reagan administration's embattled companion bill to increase tax revenues by $98.3 billion.

"Now let's pass the tax bill," shouted Rep. John H. Rousselot (R-Calif.), pointing up the difficulties the House would have in passing the tax measure if it failed to nail down the spending cuts beforehand.

Asked if the pay raise rebellion might jeopardize passage of the spending and tax measures, House Budget Committee Chairman James R. Jones (R-Okla.) would only say, "I hope not."

Some conferees had to "hold their noses" while voting for the spending cuts compromise and might want to reopen contested provisions, such as limits on federal workers' pensions, he said.

At issue in yesterday's vote was a little-noticed provision of the conferees' agreement that would authorize a special commission to recommend increases in executive, legislative and judicial salaries to the president by November.

The president could then recommend whatever increases he wanted to Congress, and they would go into effect unless both houses vetoed them within 30 days.

But Congress is scheduled to adjourn for the year by early October and not return until January unless there is a lame-duck session after the Nov. 2 congressional elections.

If the president made his recommendation within 30 days before Congress returned to town, the pay raise would take effect automatically without Congress having ever had to vote on it. Each member is now paid $60,662.

What apparently spooked the House was a "Dear Colleague" letter from Reps. Doug Walgren (D-Pa.), Patricia Schroeder (D-Colo.) and Bob Shamansky (D-Ohio) that declared in big, bold print at the top: "A vote for reconciliation the spending cuts bill is a vote to increase your own pay."

"Based on past experience," the letter said, "it is clear that the commission will most likely recommend an increase of at least 30 percent, raising congressional salaries to $85,000 a year. We find it deplorable that this pay raise is included in the very same legislation which makes cuts in programs which serve the truly needy."

The pay issue was raised only at the end of an hour-long debate on the spending cuts measure, during which little opposition was voiced to key elements of the package.

But the letter was apparently on everyone's mind, and the roll call was kept open long after it was clear that the measure would be sent back to the conferees so that members could change their votes and record themselves against a pay increase.

When the official time ran out, the vote was 209 to 191 against approval of the bill.

"It was just a whiff of panic that someone would misinterpret this provision the pay commission ," said Majority Whip Thomas S. Foley (D-Wash.), who, like most other congressional leaders, insisted that the proposal was not designed to pave the way for a congressional pay raise.

Conferees said the pay commission provision was included in the measure by Senate Majority Whip Ted Stevens (R-Alaska), a persistant advocate of pay increases, especially for upper-level government workers.

Money to finance the commission is also included in a supplemental appropriations bill now before Congress in the form of a conferees' compromise.

The appropriations measure is in trouble as well, for other reasons. Office of Management and Budget Director David A. Stockman, who had previously voiced administration opposition to the measure as over-generous toward domestic spending programs, told Senate leaders yesterday he would recommend to President Reagan that he veto it.

Administration veto threats had been more hedged in the past, and congressional leaders were hoping that Reagan would end up signing the $14 billion measure to fund the government for the rest of the year.

One Senate source theorized that the veto threat is being used to help round up support for the tax bill among conservatives who want Reagan to get tougher on spending.

There is a dispute over how quickly the money is needed. The administration contends that the Pentagon will run out of funds for military pay by the end of the month unless the bill is passed by then, but some congressional leaders question whether the money couldn't be found in a pinch.