Battle lines for the coming week's House budget votes were drawn yesterday, with President Reagan issuing a personal appeal for middle-class taxpayers to mobilize to preserve their tax cuts and House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) attempting to rally the elderly to oppose cuts in their government medical care.

The president openly joined the budget fight in his weekly radio broadcast, saying O'Neill and other House Democratic leaders are "trying to spend more and to eliminate $150 billion or so of your tax cut."

O'Neill said in a statement that the number one issue in the House debate will be "the cruel and unwarranted Republican attack" on Medicare, which he said would drive many of the nation's 29 million elderly "into personal bankruptcy."

White House aides said the president began calling fence-sitting moderate Republicans and conservative Democrats yesterday to get their support for a budget plan drafted by the House Republican leadership.

The Republican-controlled Senate passed a budget resolution Friday night that preserved Reagan's tax cuts, granted most of the spending cuts he sought, and included a $116 billion deficit.

In his address, Reagan told listeners, "If you want interest rates to come down and the economy to get going, it wouldn't hurt if you told your congressman to vote for the bipartisan recovery budget." His reference was to a plan sponsored by Reps. Robert H. Michel (R-Ill.), the House minority leader, and Delbert L. Latta (R-Ohio).

O'Neill denounced that plan, which proposes $23.3 billion in Medicare cuts over three years. Continuing the Democratic tactic of portraying Reagan as an enemy of the aged and the poor, O'Neill said the proposal "shows contempt for the old."

O'Neill said the cuts will mean "major new out-of-pocket medical expenses" for the elderly, roughly doubling their bills for a two-week stay in the hospital.

An O'Neill aide said, "The speaker thinks this will balloon up to as big an issue with senior citizen groups as Social Security is." The Democrats and lobbies for the elderly forced the administration to retreat from a proposal in the Senate budget fight to cut $40 billion over three years from Social Security.

Office of Management and Budget Director David A. Stockman said yesterday that O'Neill's figures on the effect of the Republican Medicare proposals "are manufactured out of thin air" and there is "no valid, plausible or defensible basis" for the speaker's conclusions.

Stockman said the savings proposed for Medicare would be achieved by curbing the rise in government payments to hospitals, not by raising out-of-pocket costs to elderly patients.

"As a matter of fact, the hospital cost containment savings proposed by the Carter administration with their defective plan projected even bigger savings . . . and no one said at that time that was going to come out of the out-of-pocket cost of beneficiaries," Stockman said.

Michel aide Michael S. Johnson said O'Neill's attack on Medicare proposals was expected. "They want to replace Social Security as a major political fund-raiser. . . . It's an introduction to another fund-raising effort."

White House aides said the president will intensify his personal campaign as the House begins voting this week on Democratic alternatives to the Michel-Latta spending plan and more than 70 budget amendments. They said a quick resolution of the long-running budget stalemate is essential to assure European allies and Wall Street that Reagan can still get Congress to cut spending, and reduce deficits, and as a result encourage financial markets to lower interest rates.

Continuing high interest rates in the United States, which attract foreign capital, are expected to be a prime topic of discussion at the Versailles economic summit that Reagan will attend next month.

Administration officials concede, however, that mobilizing public support to pressure Congress on the budget will be a much more difficult task than it was last year because of the state of the economy and the 9.4 percent unemployment rate.

In the radio talk, which aides said the president wrote himself, Reagan said the budget issue is "the one subject that most directly affects your pocketbook." Support for the GOP plan is critical, he said, to keep down inflation, cut spending and interest rates and "most important, get our factories working again."