Private complaints by presidential economic adviser Beryl Sprinkel about the position of the Federal Reserve Board and the Treasury that the dollar has fallen far enough typify the U.S. government's disorganization in dealing with the world monetary crisis.

Sprinkel, applying pure monetarist doctrine, wants a flood of new money pumped into the economy by the Fed. He almost surely will lose that struggle to Federal Reserve Chairman Alan Greenspan and Treasury Secretary James A. Baker III, working in tandem. But the policy malaise is not so easily dissipated. The Fed is seriously divided for the first time since Greenspan took over, and the administration has no coherent dollar policy.

There are signs of conviction at the White House that a policy is needed. It will not emerge by sending out presidential spokesman Marlin Fitzwater, no expert on currency transactions, to pledge allegiance to the dollar every time it drops in Tokyo and Frankfurt.

The feckless administration approach was intensified by everybody's absence from Washington during the dollar's post-Christmas fall. The image of no hand at the tiller was not convincing to financial markets.

Those markets have been bombarded by criticism of the Federal Reserve originating with Sprinkel, a faithful though rigid disciple of Milton Friedman's monetarist doctrine. Sprinkel is described by a colleague as in a ''blue funk,'' contending overly tight money by the Fed triggered the Oct. 19 stock market collapse and now has guaranteed a recession. According to Sprinkel, only gunning up the money supply can mitigate that economic slump.

Sprinkel and other monetarists have generated reports in the markets of a coming Armageddon between Treasury and the Fed over election-year policies. In fact, Sprinkel seems a sure loser. His criticism of the Fed is viewed by White House aides against the background that Sprinkel knows he, not Greenspan, would have been nominated to replace Paul Volcker as Fed chairman if Donald T. Regan had stayed as White House chief of staff.

Furthermore, traditional Treasury vs. Fed hostility resuming as the election nears is unlikely in view of the personalities involved. Baker and Greenspan may not be social buddies, but they have a close working relationship and are unlikely to butt heads.

The element of uncertainty is that the Fed's Board of Governors and Open Market Committee are not monoliths. Viewing an uncertain and troubling financial picture, the central bank policy makers are divided into three camps: tighteners, looseners and stand-patters (with outsiders not sure who stands where). Not for another month will the Fed's course be determined.

Widely circulated reports of Fed governors on the brink of a Solomonic decision whether to tighten, saving the dollar at the expense of the economy, or to ease, saving the economy at the expense of the dollar, are exaggerated. The consensus there is that the economy is much stronger than Sprinkel thinks and does not need a gush of money. Unlike Sprinkel, the governors agree the dollar is too low.

The internal Fed disagreement is over how much tightening the system can take and how much damage a rise in interest rates would cause. On Dec. 22, just before the latest dollar drop, supply-side economic consultant Alan Reynolds released a paper suggesting a shrinking of dollars would lower rather than raise interest rates. That theory is generally rejected at the Fed.

There is consensus at the Fed that the dollar must be stabilized by means other than the central bank's selling of Treasury bills -- diminishing the stock of dollars. While Treasury policy under Baker has been difficult to read, all signs are that he agrees the dollar is low enough. High-level, highly informal Fed-Treasury discussions have explored the dangers of a free-falling dollar.

All this puts the responsibility on Jim Baker. It will not be easy to build a new international accord. West Germany is moodily obstinate and Japan arrogantly confident (actually talking about substituting the yen for the dollar as the new world reserve currency). Baker's efforts at convening the Group of Seven finance ministers before Christmas were vetoed by the Japanese, and no new meeting seems in the offing.

But even if international cooperation were at hand, noneconomic aides to the president see benign neglect of the dollar as a policy that has outlived any usefulness and want something more than bromides put in Marlin Fitzwater's mouth. That won't be easy while the president's chief economic adviser pounds on the Fed to keep loosening money.