(FORTUNE Magazine) – ''I'M UP TO my elbows in alligators,'' says James C. Miller III, after two months as director of the Office of Management and Budget. He also has other fauna to contend with as he tries to trim some $50 billion off the 1987 budget, which has to go to Capitol Hill in early February. In his roomy office in the Old Executive Office Building hangs a serene landscape of a pastoral scene. Among the grazing creatures, says Miller, are sacred cows named Social Security and Defense. By presidential order, he won't touch Social Security funds, and defense spending will be allowed to grow at a 3% rate after inflation. Miller says he won't propose an across-the-board spending freeze but rather look at entire programs and chip or slash as needed. ''I wouldn't flinch at getting rid of programs that generate few if any benefits,'' says Miller. Some proposed cuts may surprise budget watchers. Says Donald W. Moran, a Washington consultant who worked for David Stockman, Miller's predecessor at OMB, ''Miller starts with a clean slate and can attempt cuts that Stockman and company would have thought impossible to revisit.'' Miller's budget will not include tax increases. Says Norman J. Ornstein, a fellow at the American Enterprise Institute and a Miller friend, ''He's no starry-eyed supply-sider, but he is a staunchly conservative economist who doesn't favor tax increases.'' Higher user fees for government services, such as those provided at airports and in harbors, are sure to be in the new budget; user fees are not taxes in Miller's view. As a conservative economist, he may propose turning government services and federal businesses such as the Tennessee Valley Authority over to the private sector. Another revenue-raising option: selling government assets, including Dulles and National airports and federal lands. Some of Miller's targets will be scarred survivors of previous attempts at getting domestic spending under control, most likely including the Small Business Administration, job training programs, and Amtrak. But Miller's skill at persuading legislators to accept cuts, especially those they've rejected in the past, hasn't been tested. The alligators may get him yet.