President Reagan picked up the pace of his lobbying activity yesterday, making his first public statement since he was shot March 30, as the administration pointed toward a series of showdown votes on his economic program in Congress next week.

To win approval of the president's cuts in spending and taxes, White House planners are relying heavily on Reagan's personal appeals, including a speech tentatively set for nationwide radio or television next week, and a compromise with conservative House Democrats.

Reagan's public statement came in a brief, unscheduled telephone call to a radio talk show in Beaver Falls, Pa. -- the outgrowth of one of about two dozen Reagan calls to key members of Congress seeking support for his program.

Trying to reach Rep. Eugene V. Atkinson (D-Pa.), he learned the congressman was participating in a radio show. Reagan called radio station WBVP and agreed to speak briefly on the air with Atkinson.

"Well, I'm just fine," the president began, three weeks and a day after he was shot in an assassination attempt. Reagan also got what he wanted -- a public pledge by the congressman. "I am supportive of your programs," Atkinson told the president.

Reagan got even more ringing endorsements from eight sympathetic governors who visited the White House and heard him ask for help selling his program.

Republican Gov. Bill Clements told reporters that Texas supports Reagan and that between two-thirds and three-fourths of the 24-member Texas congressional delegation would vote for the president's program. Clements said he intends to do some lobbying himself.

"I'm going to twist their arms," he said of the members of Congress. Asked if he would include House Democratic Majority Leader James C. Wright in his lobbying effort, Clements replied:

"Well, if he's got an arm."

The other governors who were invited to the White House by telephone Monday also agreed to do some persuading in their states.

Republican Govs. Robert Orr of Indiana, David Treen of Louisiana, Richard Thornburgh of Pennsylvania, James Rhodes of Ohio, Pierre du Pont of Delaware and Frank White of Arkansas took part in the meeting along with Democrat Forrest James of Alabama, who supported Reagan during the presidential campaign.

It was the first time since the assassination attempt that Reagan has met with such a large number of people.

"The president looks in fighting trim," Thornburgh said after meeting for about 35 minutes in the study in the living quarters of the White House where Reagan has been working since he left the hospital. The president has been working only a few hours a day as he recovers.

Although White House deputy press secretary Larry Speakes told reporters that "compromise is a dirty word," one move in the maneuvering of Reagan's economic program through the Democratic-controlled House has involved embracing a version of the budget plan sponsored by Rep. Phil Gramm (D-Tex.), a conservative who supports sweeping cuts in federal spending, and Rep. Delbert L. Latta (R-Ohio), a strong Reagan supporter.

"Basically, it's the administration's program with a few wrinkles," Office of Management and Budget Director David A. Stockman said of the Gramm-Latta proposal 10 days ago.

But the administration does not want to support any program that does not bear Reagan's name. Therefore, whatever the Gramm-Latta proposal is called on Capitol Hill, it is called the "Reagan-bipartisan bill" in the White House.

Stockman said yesterday that the House vote scheduled next week on this proposal would be "the real indicator as to whether or not Congress is going to go along" with the administration.

Speakes brushed off reporters who attempted to draw distinctions between the proposal the administration announced and the one drafted by the two congressmen. "We believe this Reagan bipartisan bill will give us well over 100 percent of what we asked for. We consider it our bill," Speakes said.

Latta has said that Stockman helped draft the proposal.

Reagan's voice sounded strong and unaffected by his injury in the telephone call to Beaver Falls, which lasted just under two minutes.

The president expressed thanks for the "good wishes and the prayers that I've had and the messages from the people all over the country."

The governors said he appeared vigorous at their meeting. "I thought the president looked great," Clements said. "He looked terrific, I must say," Rhodes told reporters.

The governors denied any gloom during their meeting with Reagan about prospects for the ecnomic program.

"I think he was taking inventory as he begins an offensive to get his program through Congress," James said.