The House opened debate on President Reagan's slashed-backed budget yesterday as Republican and Democratic leaders shadowboxed over whether members who vote for austerity will have to live it.

"No more fun and games," declared House Budget Committee Chairman James R. Jones (D-Okla.) in vowing to hold members' feet to the fire if they vote for Reagan's budget and then try to wiggle out of it by coming back later for more money for favored programs.

The word from the White House and the Republican leadership was far more lenient as Reagan began a series of one-on-one meetings with wavering members to shore up his support.

Unhappy Republicans are being told that a vote for Reagan's budget "does not foreclose them from voting their districts on other things," said House Minority Leader Robert H. Michel (R-Ill.).

Rep. Bill Green (R-N.Y.) returned from a chat with the president yesterday to tell reporters that Reagan reminded him that the resolution setting spending targets for fiscal 1982 will not be the last word on spending for the year. "While he didn't want to see his overall budget ceiling breached," Reagan indicated "there was plenty of opportunity in the appropriations procedure to make adjustments," said Green.

The maneuvering -- despite a claim from Michel and some conservative Democratic supporters of the president that Reagan now has enough votes to win -- indicated that neither side is confident enough of the outcome to stop wheeling and dealing.

In other developments yesterday:

The House Appropriations Committee voted to give Reagan most of the spending cuts he is also seeking for the current fiscal year in education, health and other social programs, including a 44,550-unit reduction in new subsidized housing starts for the poor. [Details on Page A6]

The chairman of the Republican controlled Senate Finance Committee proposed $1 billion more in social program cuts than the president has recommended, including a provision that would require the elderly to pay more for Medicare.

In the fight over the 1982 budget, the principal choices are a slightly revised version of Reagan's plan calling for spending of $688.8 billion and a deficit of $31 billion, and a "Democratic alternative" drafted by the Budget Committee that, with amendments blessed by the party leadership, calls for spending of $713.6 billion and a deficit of $24.7 billion. But they are based on different economic assumptions, distorting numerical comparsions.

The man differences are that the Reagan budget makes deeper cuts in social programs than the Democratic alternative and allows for Reagan's across-the-board tax cut of 30 percent over three years while the Democrats' version accommodates a smaller one-year tax cut. The Democrats on Wednesday decided to match Reagan on defense spending in hopes of attracting conservative support but dropped a plan to outflank him on the right by offering a budget that was balanced by deferring the personal tax cut for a year.

The budget sets spending targets only.Later votes will be taken on actual money bills, although the budget mandates some cuts and requires that money bills that exceed categorical targets be laid aside until a final budget is adopted. In the past, Congress has always wound up spending more than it initially budgeted.

But this year, Jones tried to insist in the opening debate, will be different. "You will look worse by being inconsistent," he said."Let's be honest with the American people."

Jones also attempted to play to some conservative members' qualms about Reagan's big across-the-board tax cut by saying they will be voting for it if they vote for Reagan's budget.

This stung Rep. Phil Gramm (D-Tex.), who accused Jones of talking about taxes to avoid having to defend the Democrats' spending plans. Gramm is a principal author, with Rep. Delbert Latta (R-Ohio), ranking Budget Committee Republican, of the Reagan budget revisions, which actually make deeper domestic spending cuts than Reagan himself proposed.

Latta, in turn, tried to play off the President's popularity. "I happen to believe the American people elected Ronald Reagan chairman of the board and president of the United States," he said.

Meanwhile, the vote predictions continued. Michel said Reagan has the "solid" support of 35 Democrats, enough to win. He said not more than one or two Republicans "will be willing to stand that spotlight of publicity" that would come with voting against Reagan.

But Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) said as many as 16 Republicans may defect and, abandoning his pessimism of earlier this week, said Democratic chances "look a lot better" because the impact of the proposed spending cuts is sinking in.

"It's suddenly hit home out there," he added.

Said Jones: "Neither side has the votes yet."