Congress is living up to its promise of quick action on the drought, assembling a $3.9 billion relief bill for President Reagan's signature with a speed seldom matched since the New Deal was hatched.

The bill is the most generous disaster package ever for agriculture. It includes an extra dose of help for farmers with the worst crop losses, a three-month increase in the milk support price and rewritten livestock aid programs.Despite the bill's magnitude, aid is likely to fall short of the losses farmers suffer. The Agriculture Department, for instance, has projected U.S. grain production may be only three-fourths of last year's.

Senators unanimously approved the compromise bill 92-0 Monday. The House was expected to call the bill Tuesday with overwhelming approval likely.

President Reagan already has signaled his support for the legislation. Congressional leaders said the president might be able to sign the bill later this week - just one month after the legislation was filed in Congress. Major legislation rarely moves that quickly.

Agriculture Department officials say it will take about 60 days to implement the bill and begin delivering aid to farmers. Sen. Patrick Leahy, D-Vt., called the legislation "a compassionate response from the heart of the American people."

The centerpiece of the bill is disaster payments to farmers for losses that exceed 35 percent of a crop. The payments would be figured at 65 percent of the usual price for crops, as set either from federal farm programs or the average price in the past.

Aid also would go to livestock producers and dairy farmers. Farmers also will be encouraged to plant more soybeans, sunflowers and oats next year.

Although the bill's price tag is set at $3.9 billion, the amount actually spent may vary. The exact cost will depend on how much damage is done to American agriculuture.