In each of the last three years, the Reagan people have fretted publicly about an unpleasant "October surprise." In 1980 and 1981, they avoided it. This year, it may catch up with them.

The original "October surprise" was the possibility that President Carter might engineer some last- minute deal on the Iranian hostages, and thereby snatch victory from defeat in the presidential race.

In the summer of 1981, White House Chief of Staff James A. Baker, III, began talking about a second "October surprise," a possible public backlash against the Reagan budget cuts. Baker was preparing for a possible slump in Reagan's polls, and even some reverses on Capitol Hill. But the congressional support held firm, and when the polls dipped, it was more because of the interest rates than spending cuts.

This time, the focus is the Oct. 8 unemployment report. The White House fears that this will be the report announcing double-digit joblessness.

"I can just imagine what the first eight minutes of the television news will be when unemployment breaks through 10 percent," said one White House official. "It will be 71/2 minutes of pathos, and 30 seconds of us saying we're sorry for people's suffering, but we're sure there will be better times."

This is more than a public relations problem, as even the politicians in the White House acknowledge. Despite the September rally on Wall Street, this is still a very sick and sluggish economy.

In the face of that reality, it is a matter of wonderment to many of the president's men that people are as patient as they are. By substantial majorities, the voters are telling the pollsters they expect things to improve in the next couple of years.

Part of that patience stems from the fact that substantial numbers of Americans are prospering under Reaganomics. Those in their middle years with paid-down mortgages and secure jobs are benefiting from the cut in taxes, the decline in inflation and the incentives to savings.

Equally significant has been the patience of millions who say that their economic situation has worsened since Reagan became president but have been willing to give his program more time. It is their confidence that White House officials think may be jarred by the Oct. 8 report.

Related fears are expressed by senior Republicans. One is that the Democrats, after 21 months of ineffectual muttering about Reaganomics, may finally have found their voice. One top GOP strategist was openly admiring of the new Democratic National Committee commercials, especially one showing a champagne-like gush of tax benefits filling the crystal glasses of the rich, while the worker below gets a few drops of tax relief in a tin cup.

"Nobody knew what trickle-down meant," this official said, "until this commercial showed it. If they had $10 million to put these ads on the air, they'd cut us to shreds."

In their new nervousness, the Republicans worry even about Reagan. He is talking much more about abortion, school prayer and other New Right social issues than he is about the economy, and those issues are either irrelevant or harmful when the public is almost totally fixated on the economy.

So October is worrisome once again. And this time, maybe, for good reason.