Many major bankers fear that it will be difficult, or impossible, to meet loan commitments they have made to their business customers and comply with the Federal Reserve dictum that loans should grow no faster than between 6 percent and 9 percent this year.

In early January, loan commitments to businesses were already at a high level, and those commitments grew sharply in late February and early March after rumors began to circulate that President Carter would impose some form of credit controls.

Businesses went out and hit up their bankers for increases in their credit lines so they wouldn't be cut out if the president invoked lending restraints -- as he in fact did on March 14.

"These weren't the kind of companies you could say no to. These were the name corporations in America," said the chief lending officer at a major bank.

Bankers say privately that they feel they will be caught between the Scylla of their promises to their customers and the Charybdis of the Federal Reserve regulations.

"We could well be placed in the unenviable position of either going back on our word to our customers or facing the Fed's wrath. And our word is bond," said the top lending officer at a major money center bank. "We would not stay in business long if we promised our customers credit, made them pay for their lines, then told them the funds were not there when they asked for them."

Critics who believe that big bankers -- or for that matter, small bankers -- played a significant role in the speculative boom that helped feed the current inflation don't mind seeing them squirm now. Government officials and others blame the banks for feeding speculation by supplying huge amounts of credit to finance corporate takeovers, commodity speculation and excessive purchasing by consumers.

At the same time, however, bankers have the critical role of fulfilling legitimate borrowing needs for businesses. If credit is unavailable, or severely restricted in the coming months, the recession that was foreordained (although months late) will be much worse than it has to be, many bankers say.

Although loan demand declines during a recession, it usually increases -- sometimes sharply -- during the early stages as businesses are forced to finance inventories they no longer can sell. For example during the severe recession of the mid-1970s, it was not until the spring of 1975 that loan demands declined noticeably, although the recession took hold in the fall of 1974.

This year the strain that businesses could put on their bankers may have been greater than in 1974 and 1975. A chaotic bond market -- record high interest rates -- have kept many companies borrowing short term from their banks rather than selling long-term debt securities to the public.

According to a Chemical Bank survey of 135 major banks, loan commitment totaled $379.6 billion at the end of January, while only $138.5 billion of those credit lines had been tapped.

Between the end of January and early March, companies added to those lines at levels that can be measured in the tens of billions of dollars, according to Edward Palmer, chairman of Citibank's executive committee.

Chemical Bank said "there is a real possibility that massive and sudden increases in bank loans could occur," although that is not its most likely scenario for 1980.

But if the bond markets remain unsettled and the nation's corporations find themselves stuck with goods they cannot sell, then banks likely will find themselves besieged by businessmen who want to draw on their credit lines.

During the 1974-75 recession, businesses increased their use of credit commitments to 45.7 percent of their outstanding lines, according to Chemical Bank. At the end of January, businesses had drawn only 36.5 percent of their available lines.

If businesses should behave as they did in 1974-75, even ignoring the large increases in commitments that occurred in late February and early March, then business loans "could surge by some $35.5 billion," the bank noted. That is equivalent to 20 percent of the outstanding loans.

Not all bankers are pessimistic. Many feel that they will be able to satisfy their customers' needs by tapping smaller banks whose credit demands aren't as strong as at major banks. But parcelling out loans in small packages is a time-consuming and expensive way to do business.

Other say they hope that the recent stability in the bond market will convince some of their customers to sell debt securities rather than borrow from their banks, even though interest rates remain at near-record highs.

Nonetheless, most bankers feel itchy. The longer it takes the nation to slide into a recession, the longer it will be before loan demand subsides.

At a time of high inflation -- when it takes a bigger loan to finance the same physical amount of inventory than it did a year ago -- a ceiling of between 6 percent and 9 percent on loans increases looms as a difficult, if not impossible, goal.