President Reagan's chief spokesman yesterday shrugged off the first potentially damaging poll to appear since Reagan's inauguration with an assertion that the president believe the people support what he is doing.

White House press secretary James Brady said that a new Gallup Poll showing Reagan's disappoval rating at 24 percent, while his four most recent elected predecessors all had disapproval ratings of 9 percent or lower two months into their administrations, results primarily from Reagan's economic program.

Brady told reporters that none of the other presidents had spelled out such a controversial program at this point in their administrations and it was to be expected that some groups would express disapproval.

However, he said that Reagan believes he is "hearing a contradictory message from the people." Brady cited mail to the White House as one evidence of support for the president. He said the White House has received 30,690 letters in favor of the president's program of tax and spending cuts and only 285 in opposition.

Asked how he could square that mail count with the Gallup Poll, Brady said: "How does it fit? We'll go with our mail."

Brady said the poll results would not affect administration policy in any way. "If anything, we'd say this was expected," he added, but he did not directly answer a question about how the administration could expect such a poll result at the same time it believes its mail shows Reagan has over-whelming support around the country.

One Reagan administration program is garnering more support than was asked for.

Nancy Reagan's plan to renovate the living quarters of the White House with $200,000 raised from private contributors has brought an outpouring of gifts that totaled $375,528.80 as of March 12, according to Sheila Patton, Mrs. Reagan's press secretary.

White House officials refused to make public the list of 167 donors, but said that many large contributions came from foundations as well as individuals.

Patton said the excess money will go to the White House Historical Association to be used in its ongoing program of redecoration of the public rooms. Some people close to the project have said privately that the cost of renovating the family quarters could run to almost $600,000, but Patton has said that $200,000 is the target.

In other developments, Reagan authorized using money from the President's Disaster Relief Fund to assist with sewer and street repairs in Louisville following sewer explosions Feb. 13. By declaring that the sewer explosions constituted a major disaster, Reagan made available federal funds to pay three-quarters of the repair costs. r

Reagan also announced three choices for senior government posts:

William H. Draper III, a venture capital investor from Palo Alton, Calif., to head the Export-Import Bank. Draper, 53, has long been an active Republican, but apparently only recently became a Reagan Republican.

A. James Barnes, 38, to be general counsel of the Agriculture Department. He is a partner in the Washington law firm Beveridge, Fairbanks & Diamond.

Loren A. Smith, 36, to be chairman of the Administrative Conference of the United States. Smith is a professor at the Delaware Law School, Widener University.