President-elect George Bush has been given the glum news that the budget deficit in the next fiscal year will be $21 billion higher than the Reagan administration had previously estimated. That information means that Bush will be facing an even bigger budget headache when he takes office on Jan. 20. The new deficit estimate was presented to Bush and President Reagan during a Cabinet briefing Thursday on the administration's final budget submission to Congress. Joseph Wright Jr., director of the Office of Management and Budget, said the OMB now estimates that the deficit for the 1990 fiscal year, which begins next Oct. 1, will be $132 billion, substantially higher than the $111 billion deficit estimate OMB made just three months ago. Officials said the main factors boosting the deficit estimate were the drought, which slowed economic growth this year, and higher-than-expected interest rates, which raised the cost of financing the $2.6 trillion national debt. The Gramm-Rudman balanced budget law's deficit target for 1990 is $100 billion, which means that $32 billion in budget cuts will be needed to close the gap between revenues and spending. Achieving such sizable cuts in the face of congressional opposition to further reductions in domestic programs will present Bush with major political problems. During the campaign, Bush sidestepped specifics on how he would deal with the budget deficit by touting a plan for a ``flexible freeze.'' Bush said he would allow government spending to grow only enough to match inflation. Within the overall freeze, selected programs could grow while others would be cut. However, Bush avoided providing details on what programs he would cut in order to free funds for increases that he promised to make in education, child care and health care for the poor. The budget document Reagan sends to Congress on Jan. 9 will reflect his decisions, presidential spokesman Marlin Fitzwater said. However, officials said it was likely that Bush would rewrite at least part of the document once he takes office, just as Reagan did in 1981 when he submitted his own budget to Congress in place of the budget left behind by President Carter. Officials refused to comment on reports that the final Reagan budget will call for substantial increases in defense spending and steep cuts in domestic programs as a way of providing Bush with the opportunity to present a ``kinder, gentler'' budget blueprint once he takes office. OMB spokeswoman Barbara Clay said that Reagan's final budget would not include any tax increases, something the president has consistently opposed, or seek to trim Social Security benefits as a way of meeting the $100 billion Gramm-Rudman deficit target. ``We have some difficult choices ahead'' on where to cut spending, she said. With estimates on future deficits rising, many private economists are convinced that Bush will be forced to accept some type of tax increase despite his oft-repeated opposition to new taxes during the campaign. As examples of pressure for increased spending, they point to public demands that the government do more in the fight against drugs, and to estimates topping $50 billion for the cost of bailing out hundreds of insolvent savings and loan institutions. House Speaker Jim Wright on Thursday said that the first signal on whether Bush is serious about reducing the budget deficit is likely to come from his appointment of two members to the National Economic Commission, a bipartisan advisory group created to come up with a blueprint for eliminating the budget deficit. Bush criticized the commission during the campaign as a device for raising taxes, but Wright said if Bush is serious about dealing with the deficit, he will weigh carefully his appointments, which are expected to be made soon. ``Will they be pragmatic people, will they be realistic people, will they be people dedicated to finding a true solution to this enormous budget crisis?'' Wright, D-Texas, asked. ``I think that may be his first signal.'' Also providing hope to some that a resolution can be reached in the seven-year budget deadlock is the widespread expectation that Bush will name Richard Darman as the new budget director. Darman, a longtime aide to former Treasury Secretary James A. Baker III, is considered a pragmatist who would seek to work with Congress in crafting deficit-cutting solutions. Wright repeatedly refused to offer his own view on how to make the needed budget savings although he said he had many questions about how Bush's flexible freeze would work. ``I have an open mind and I'm willing to listen to the president's refinement of exactly how he interprets the meaning of that phrase,'' Wright said.