President Reagan's budget policies drew new bipartisan fire yesterday as an influential Republican joined Democrats in suggesting that the administration deliberately fosters high deficits in order to "bleed" domestic spending programs.

At a Senate hearing on confirmation of James C. Miller III as director of the Office of Management and Budget, Sen. David F. Durenberger (R-Minn.) said he is coming "dangerously close" to ascribing to the theory that "there is some deliberate intention to use deficits . . . to get us to denationalize the financing of public services."

His comments followed a similar suggestion from Sen. Thomas F. Eagleton (D-Mo.) during Miller's confirmation hearing before the Senate Governmental Affairs Committee and previous charges by Sen. Daniel Patrick Moynihan (D-N.Y.).

Asked by Eagleton if he could refute the charge, Miller said, "I cannot absolutely refute it because I wasn't in their minds." Miller served as regulatory administrator for OMB for nearly a year before becoming Federal Trade Commission chairman.

Durenberger, a member of the Finance and Governmental Affairs panels, said after the hearing that the notion of deliberately created deficits is gaining currency in Congress as Reagan continues to emphasize other issues, such as tax-law overhaul, over deficit reduction.

"Why is he on tax reform when he should be on deficits? Why does he undercut the Senate budget resolution?" asked Durenberger in reference to Reagan's spurning of a Senate budget that would have raised taxes and cut Social Security to achieve larger long-term deficit reductions than Congress ultimately approved.

Similar rumblings on the deficit issue came during the weekly Senate Republican caucus luncheon dominated by appeals for further action to contain deficits. These included interest in a plan by Sens. Phil Gramm (R-Tex.) and Warren B. Rudman (R-N.H.) to force spending cuts sufficient to balance the budget by fiscal 1990.

The plan, expected to be offered as an amendment to debt-ceiling extension legislation next month, would set various restraints on spending to reduce the anticipated $172 billion deficit for next year by about $43 billion annually over the next four years. If all else fails, spending would be squeezed under target numbers by forcing an across-the-board "sequestering" of funds in all budget accounts.

The Gramm-Rudman plan is one of at least four deficit "sweeteners" headed for attachment to the debt measure, which would raise the federal debt ceiling to $2 trillion, double its level of five years ago, to accommodate huge deficits.

Other sweeteners would do the same thing in different ways, mainly through mandating spending cuts and strengthening presidential powers to withhold spending.

Under questioning, Miller said he supports major deficit-reduction efforts, possibly including cutbacks in major benefit programs, but warned against "precipitous" action that might unsettle the economy.

He hedged most of his comments with caution not always observed by his outspoken predecessor, David A. Stockman, emphasizing that he would "follow the president's policy" on all counts.

Earlier this year, Reagan scuttled an effort to cut back the biggest benefit program, Social Security, when he disavowed a Senate Republican plan, developed with Stockman's help, to restrain Social Security cost-of-living increases.

Miller echoed Reagan arguments that economic growth will be a major factor in reducing deficits but, under pointed questioning from Democrats, said that "it's probably unreasonable to assume mere growth in the economy" will eliminate deficits over the next decade.