Demonstrating renewed sensitivity to the accusation that his economic policies are unfair, President Reagan charged yesterday that his Democratic critics would lead the nation "right back to the same swamp that we're trying to get out of."

"They're not promoting fairness," the president said at a Republican fund-raising reception here. "They're selling the same old snake oil."

Republican surveys have shown consistently that the administration is most vulnerable on what White House officials call "the fairness issue." Reagan's eight-minute speech, ostensibly a pep talk on behalf of Rep. David F. Emery, the Republican nominee for the U.S. Senate in Maine, showed a high awareness of the potential potency of this issue in the midterm elections.

"The air is filled with liberal voices talking big talk about fairness and compassion," Reagan said. "They would urge the American people to turn their backs on everything that we've accomplished together. And to listen to their horror stories about budgets, you'd have to like horror movies."

It was not one of Reagan's most effective performances, an aide acknowledged afterward. The president stumbled verbally a couple of times during the speech, once ruining the punch line of a story by saying "recession" when he meant "depression." He also acknowledged that unemployment had increased during his presidency.

But the president's speech, at the Hyatt-Regency Hotel, accomplished its principal objective, which was to raise an estimated $100,000 for the beleaguered Emery, once 36 percentage points ahead of incumbent Democratic Sen. George J. Mitchell and now 4 points down in GOP polls.

The White House view is that the Emery campaign has stabilized and that he can win if he raises another $250,000 to go with the $750,000 he has spent. An administration official said yesterday that Emery can "leverage" the $100,000 Reagan raised for him yesterday to make up the difference.

Reagan did not go to Maine, according to this official, because "the fund-raising sources there have been tapped dry." The contributions yesterday were made by business political action committees, who paid $500 to $1,000 a ticket for the event.

Many of the tickets were given to young staff members of Republican members of Congress and GOP volunteers, who dutifully cheered and applauded the president's defense of his economic program.

Reagan contended that the administration had made "solid progress" in dealing with high interest rates and inflation, which he called "the two biggest barriers to a growing economy." He also reflected continuing concern about unemployment, which the administration expects to reach 10 percent when the September jobless figures are announced Oct. 8.

"The greatest challenge we face is to get unemployed Americans back to work," Reagan said.

The greatest challenge Emery faces is to avoid becoming unemployed himself and get his campaign rolling again after a year-long series of campaign blunders that changed him from odds-on favorite to underdog against Mitchell.

Despite all that has happened to Emery, the administration assessment is that he has the second-best chance of any Republican challenger to oust a Democratic incumbent. The best chance, administration strategists say, is in Nevada, where Republican challenger Chic Hecht faces incumbent Democrat Howard W. Cannon.

Reagan and his cautious White House advisers are rationing the president's campaign appearances carefully. But his speech today was considered vital help for what remains the administration's No. 1 political goal, which is keeping Republican control of the Senate.