As Vice President Bush was hailing the Senate for virtually rubber-stamping the administration's budget-cutting plan, House Democrats were indicating yesterday that they may depart in significant ways from the Senate model as they begin their round of the budget battle next week.

House Budget Committee Chairman James R. Jones (D-Okla.) told reporters that, while he agrees with the president's goals and supports "certainly over half" his specific proposals, he expects to propse changes when he presents his own budget recommendations to the committee Monday.

One of those proposals will involve savings over the next three years of $10 billion by curbing "waste and inefficiency" in government, Jones said, embracing a cause that many Republicians, including Reagan, championed when the Democrats were in power.

Jones said he expects to include savings of $4 billion for fiscal 1982 from improved debt and tax collection, paperwork reduction, follow-through on audit reports and related cost-cutting endeavors in his budget proposal Monday.

Sources said Budget Committee Democrats have also tentatively agreed to a cutback of $4.6 billion in defense spending for fiscal 1982, subject to change Sunday as they continue meeting with Jones on the final draft of his budget proposal.

The Senate ordered its Armed Services Committee to make less that $1 billion worth of cuts in defense spending in the $36.9 billion package of "reconciliation" instructions to legislative committees that it adopted Thursday in the first phase of congressional action on Reagan's proposed budget cuts.

It was this floor action that Bush hailed in a visit to Capitol Hill, aimed both at bestowing Reagan's tribute on the Senate and at nudging the House to follow in its path.

The Senate has set an "example" for the Hose, Bush noted as he appeared before television cameras to appraise both Republicans and Democratic leaders who helped steer Reagan's program through the Senate.

It was largely because of the defection of conservatives that Democrats failed in the Republican-controlled Senate to leave much of any mark on Reagan's progam, and Democrats in the House, although they have a nominal majority of 242 to 191, have a less extreme but similar problem.

Jones, who was supported by conservatives in his campaign for the committee chairmanship last year, is walking a fine line between the left and right wings of his party, both of which are crucial to the Democrats' chances having much influence on the budget. As a result, he met for several hours Thursday and yesterday with Democratic members of the committee and plans another session Sunday.

"We've got to have a consensus package or we're out of the game," said Rep. Leon E. Panetta (D-Calif.), member of a moderate group on the committee that's been working closely with Jones in developing his proposal.

The Democrats have been considering restoring money for a number of programs targeted for sever cuts by Reagan, including energy conservation and development, nutrition, education, health, social services, research, mass transit and job training. But they have also been trying to avoid exceeding Reagan's deficit figure of $45 billion for next year.

Among other things, they are considering less of a tax cut than Reagan wants. Jones indicated yesterday that he is likely to be more pessimistic that Reagan in his economic assumptions (although less pessimistic than the Congressional Budget Office), which could have an effect on both tax and spending targets.

Among the savings anticipated by Jones from controlling "waste and inefficiency" are roughly $600 million from defense, on top of the $2.9 billion that Defense Secretary Caspar W. Weinberger has included in his 1982 budget proposal.

Other savings include $1.1 billion from improved collection of debts, $700 million from collecting unpaid taxes, $1 billion from following through and audit recommendations and $300 million from reducing paperwork.

Analyses from Congress' General Accounting Office, upon which the recommendations are partially based, "paint an appalling picture of mismanagement, lack of management, indifference and outright abuse of public trust," said Jones.