The prime rate that banks charge some of their best corporate customers for borrowing may fall this week at a number of institutions.

But don't expect any substantial reduction in this closely watched interest-rate barometer, which has lost much of its economic bellwether status during the past two years because fewer and fewer loans are being made at this rate.

And don't give any credit for a reduced prime rate to edgy Republican congressional leaders, who last week borrowed some pages from the populist politics of the late Wright Patman and from the comedy of Rodney Daingerfield.

Just as the long-time House Banking chairman once railed against banks for high interest rates, so did Rep. Bob Michel (R-Ill.) and some of his colleagues take on Wall Street last week.

Unless the bond and stock marketsbegin to show a little respect for the Reagan administration's economic program and unless interest rates fall, dire consequences of credit restrictions and financial institution regulations could follow, they warrant.

Currently, most Washington and national banks have their prime rate at 20.5 percent. Chase Manhattan Bank and First National Bank of Chicago cut their rates to 20 percent at the end of August and Marine Midland of New York moved to the lower rate last Friday.

Because some other short-term interest rates have declined, more banks are expected to bring the prime rate down. But bankers are working in a new era of financial competition, and they are still trying to figure out how to sustain profitability from a new mix of service charges and high rates they must pay to attract funds for lending.

Unlike earlier periods of high rates, most banks have not been doing so well in 1981, in terms of profits.

Bank of Virginia Co., one of that state's largest financial institutions, is a good example of how bankers are trying to cope in this new world. In an effort to understand its market more thoroughly and ultimately to increase deposits, Bank of Virginia recently hired a research firm to conduct a broad statewide survey that showed most consumers generally are loyal to their original choice of banks.

Moreover, the survey showed that customers believed you don't get something for nothing. They do expect professionalism, good information and advice about financial services that best meet their needs, however.

Last fall, Bank of Virginia began a major business restructuring "to meet the demands of a changing marketplace," said executive vice president Donald R. Just. Ten unprofitable branches were closed, several departments were consolidated, controls were placed on noninterest expenses and unprofitable lines of business were curtailed.

As Just explained it, banks still operate under rules that were designed for the 1930s, and many institutions that traditionally have been consumer banks often find themselves with more fixed-rate assets than fixed-rate liabilities. Funding fixed-rate loans with money purchased in the open market today has become very expensive. At the same time, banks are losing deposits to money market funds and other investments.

Bank of Virginia's restructuring eliminated 348 positions. Through attrition and transfers, only 84 employes lost their jobs. "Naturally, we are not pleased that anyone had to lose a job but are gratified this number was reduced," Just said.

And now, the bank firm is concentrating on building more profitable business. As a result of the survey, consumers are being offered a number of new products. For example, Bank of Virginia has started "relationship banking," a service that takes into account other deposit balances when assessing service charges on checking. Under this new system, customers have at least nine ways to eliminate services charges on checking accounts.

Another new service is a method of handling inadvertent overdrafts. When a customer provides the bank with a telephone number, they will receive a direct call from their branch so arrangements can be made to cover checks and prevent a bounced payment.

Finally, as a result of the survey, a representative group of tellers from each city across the state met with management and offered candid comments about the bank. It was the consensus of the group that the bank needed to do something spectacular to let the public know about the changes.

The group requested career apparel and recommended the styles, designs and colors. As a result, every teller throughout Virginia was wearing a new look starting last week. It may be the first time in banking history that tellers are wearing uniforms that look much like airline stewards or stewardesses.

Some people took the comments of Michel seriously last week. The gold bugs, always sensitive to the possibility of economic chaos, pushed up the price of gold to a Friday close in London of $448.25 from $439.50 a week earlier. Stock prices also rose and the long bond market slide was halted.

These trends could be reversed this week, because the administration is continuing to send out conflicting signals on the economic future.

President Reagan decided on Saturday to reduce increases in defense spending by just $13 billion over the next three years, a lot less than many people in the financial markets had expected and desired. Now, proposed spending cuts will have to be concentrated in other federal programs if overall goals of restraint and a balanced budget are to be met. That points to another protracted political struggle, the outcome of which is never clear.

Such uncertainties are bound to depress the financial markets, and there are two time bombs ticking that add to this problem.

The first time bomb is next year's congressional elections. Republicans are concerned about their prospects if record interest rates continue much longer, further destroying the housing and automobile markets.

In addition, pollster Louis Harris told a Yale University audience last week that based on a close reading of the polls, the American people are willing to give Reagan's supporters in the business community no longer than the fall of 1982 to get the economy's house in order.

"If, by this time next year, inflation is not below 10 percent, if the prime rate on borrowing is not down to 11 or 12 percent, if capital investment is not up sharply, if new technology is not being infused into the industrial process, and if the federal budget is not well on its way to being balanced, then the patience of the American public will be stretched to the breaking point," he said.

According to Harris, businessmen are dismayed by this scenario because they know it will take years to achieve such goals. Thus, he said, it is probable that by next fall a dramatic new issue will emerge in the United States. Harris forecast a great deal of criticism of management, of business schools and the scientific community under a gerneral problem he called "the management crisis."

If public patience runs thin, Harris said we are very likely to see a very different role for government. "Rarely has American business had thrust upon it so sudden and sweeping a mandate," he added.

If there is no progress in restoring economic health, Harris listed a number of potential questions that will be raised. Some of the issues of the 1980s, Harris said, are:

* Should government set targets, monitor and even participate in the capital formation process?

* How can government help restore the scientific and technological capabiltity of American industry?

* How can government monitor and assist in setting targets and rates for progress toward turning around lagging productivity?