Washington — Through what it calls ''honest budgeting'' - cutting back on a few programs, being forthright about the actual cost of the rest, and improving Pentagon management - the Reagan administration hopes to convince lawmakers and the public that more sharp increases in defense spending are justified.
Congress and the President recently agreed on a $200 billion military budget for fiscal year 1982. It is expected that the administration's figure for 1983 (to be announced in about a month) will rise by at least 15 percent, which includes inflation plus a ''real'' increase of 7 percent as has been promised.
The political challenges are formidable. Such increases can only come at the expense of social programs (including the extremely sensitive entitlement programs which benefit middle-class people as well as the poor). This is an election year, and polls indicate a softening in public support for an arms buildup despite Poland, Afghanistan, and other hot spots around the world.
Some of the Pentagon's staunchest friends on Capitol Hill are warning of the economic and political consequences of spending more for defense without clear improvements in efficiency.
''There is serious doubt that all of the new programs being discussed are affordable,'' Sen. John Stennis of Mississippi, ranking Democrat on the Senate Armed Services Committee, has warned. ''Public support of the military and the military budget will evaporate quickly if our military forces do not show real improvement without damaging the health of our economy.''
This realistic view is shared by those in the administration responsible for planning defense spending. They acknowledge that the infamous cost overruns and deliberate underfunding must stop if they are to hold support for a bigger military.
''The principal failing of the system has been to 'buy in' to the budget, to underfund,'' says Deputy Defense Secretary Frank Carlucci, No. 2 man at the Pentagon. ''Given the resources that we have, we have too many weapons systems because of this tendency to underfund. That's the single most pernicious thing that leads to a loss of confidence.''
There is general agreement on this point. The budget battle in 1982, however, will focus on the administration assertion (as Mr. Carlucci puts it) that ''you don't measure defense against social programs, you measure it against the threat.''
It will also hinge on how well the administration has done in its first year of trying to improve Pentagon management, particularly the acquisition of expensive weaponry, which makes up more than half the defense budget.
While it wants to spend some $160 billion more than Jimmy Carter had planned for defense over the next five years, the Reagan administration has reduced or canceled more than 60 weapons programs. That should mitigate some of the rearmament effort by several billion dollars.
Together with a pay cap and trimming such symbolically annoying things as questionable travel and consultant costs, the administration plans to save $31 billion in Pentagon spending over the next five years.
But there are even larger and more permanent savings to be found through eliminating waste and mismanagement, critics point out. The General Accounting Office has hammered away at this issue for years, and the conservative Heritage Foundation puts the potential annual saving at $10 billion. The Republican Study Group says $16 billion.
As chief budget writer and spending watchdog at the Pentagon, Mr. Carlucci has initiated a 32-point management reform program aimed at this institutional fat, particularly in the buying of weaponry.
He points to multiyear funding (to provide greater stability and economy), better auditing, letting more contracts through competition, and using a more realistic inflation figure among efforts at ''honest budgeting.''
''There are no panaceas, but we know we are on the right track,'' he said recently.
The Reagan administration has embarked on the nation's largest peacetime military buildup, one totaling some $1.5 trillion over the next five years. But it knows that without substantial cost-effective reforms, its public mandate and the congressional support that mandate has thus far generated could quickly wither away.