President Reagan declared himself "rarin' to go" today as he renewed a campaign to overhaul the federal tax system by comparing himself to Harry Truman and quoting from a Democratic report favoring his tax plan.

Speaking in the courthouse square of the city where Truman began his political career, Reagan launched what aides said will be a month-long campaign with a bipartisan appeal.

Citing a report of the House Select Committee on Children, Youth and Families that Reagan said favorably described his proposal as "pro-family," the president said: "That sounds like a pretty fair appraisal and it doesn't come from my party, it's coming from the majority party, the Democrats. On this I'm happy to say we're not Republicans or Democrats, we're Americans -- and we've got something to do for America."

Reagan, looking fit and rested after a 23-day California vacation, was greeted by a friendly and enthusiastic crowd of several thousand people jammed into the shadeless square in sweltering heat. Before he began, Reagan peeled off his blue-and-white sports coat, setting an example that was quickly followed by other politicians on the speaker's stand.

Reagan, who has been in virtual seclusion since a cancerous tumor was removed from his colon on July 13, said he had missed campaigning, even the hecklers. But he said the opponents of tax reform hadn't missed his absence.

"Those vested interests just hate it when we talk about reform, and they loved it when they thought I was laid up and out of action," Reagan said. "Well, I'm back, and rarin' to go, up for the battle that has only just begun."

Reagan, who rode a horse at his ranch northwest of Santa Barbara six weeks after his operation and who spoke vigorously today, has a busy September schedule, including weekly trips to different regions of the country in behalf of the tax bill. Presidential aides say he will be X-rayed soon after he returns to the White House to make sure that there is no sign of further malignancy.

In his speech here, the president emphasized the theme of "fairness," which advisers have said will be the major element of his tax-overhaul campaign.

The speech also advertised the administration's dependence, at least on tax issues, on the House Democratic leadership. Reagan is counting on Rep. Dan Rostenkowski (D-Ill.), chairman of the House Ways and Means Committee, to push the tax-overhaul bill through the House, and the president's speech today eschewed partisan rhetoric in favor of denouncing unidentified "special interests."

The president said his proposal was opposed by lobbying groups "who share a kind of self-righteous self-interest" because their clients benefit from advantages in the present tax code.

When he unveiled his tax plan in a nationally televised speech May 28, Reagan called it the "second American Revolution" and emphasized the simplicity of his proposal as well as its fairness. Critics of the proposal, however, have contended that it does not really simplify the tax code, and Reagan made only a passing and indirect reference to the "simplification" argument today.

But while polls show widespread support for the generalized idea of "tax reform," even Reagan acknowledges that it is not a burning issue for many Americans. He said that one of the reasons the tax structure hasn't fundamentally changed is that "in a democracy like ours, it's hard for us to get worked up and united over something unless it's truly dramatic like a sensational murder."

"Well, our tax code is not a sensational murder -- it's more like a daily mugging, and we've begun to get used to it," Reagan said.

In a reference to Truman, Reagan said, "I'm proud to be talking about this good deal in the home of the father of the Fair Deal. I just figure we're taking another step toward independence in Independence. I think Harry would be very pleased."

Reagan, a longtime Democrat, campaigned in 1948 for the election of Truman, who scored an upset victory over Republican Thomas Dewey. His vote for Truman, Reagan has said, was the last he ever cast for a Democratic presidential candidate although he did not become a registered Republican until 1962.

The president is scheduled to continue his campaign for tax revision Thursday with a trip to Raleigh, N.C., where he will speak at North Carolina State University.