In the name of "the little saver," the country's biggest banking groups are besieging Congress to approve a new tax exemption -- this one on interest from savings accounts.

Trade associations for banks and savings and loan institutions have activated their nationwide networks to push for passage.

As a result, before 26 senators and House members sit down this week to confer on an oil-profits tax, they'll find their mailboxes and phone lines jammed with messages from the bankers back home.

The message has nothing to do with oil profits. Rather, it hails a Senate-passed amendment to the oil tax bill that would exclude some savings account interest from federal income taxes.

The source of lenders' enthusiasm, clothed in the apparel of helping folks with small savings, is no secret. They see the tax break as a way of enticing money from other sources into savings. Savers might benefit but so would bankers, with more money to lend and profit on.

Another point is equally clear. As an amendment to an oil-tax measure the president and others dearly want, the proposal's political chances are enhanced.

Savings-account interest became an issue for this conference after the Senate last month added language by Sen. Lloyd Bentsen (D-Tex.) to exclude from income tax the first $201 a saver earns in interest.

For banks and savings and loan associations, it's almost a dream come true. For years they have been pushing for the exclusion in hope of attracting more money to savings accounts.

Since the House oil-tax bill has no such provision, the banking groups are aiming their lobbying guns at House conferees who will have to accept or reject the Bentsen proposal.

A pending House bill dealing with mortgage bonds carries an amendment by Rep. W. Henson Moore (R-La.) that would exclude just the first $100 in savings interest from income taxes.

But for now, the big fight will be in the oil-tax conference, and Moore said last week that he is campaigning to get fellow House conferees aboard the Bentsen bandwagon.

"The exclusion is very necessary to help reverse the trend of declining amounts of money going into savings accounts and to help stimulate capital formation," Moore said.

"This is a political opportunity to form capital and fight inflation and get people saving more money again . . . The exclusion ought to be higher, but this is a foot in the door. If this passes, we can then work on something more meaningful for the future."

That is precisely what the Carter administration, many House tax-writers and tax-reform groups fear -- that once the exclusion is adopted, it will lead to even greater write-offs that would reduce tax revenues.

Bentsen's amendment also allows exclusion of $400 of interest when joint tax returns are filed. His exclusion applies to savings interest as well as stock dividends -- one, the other or a combination. Current law allows individual exclusion of $100 and joint exclusion of $200 on investment dividends.

Opponents have argued that if savings incentives and capital formation are the issue, as Bentsen and Moore contend, they ought to be dealt with separately and not as appendages to other bills.

Moreover, there is concern about the cost of the Bentsen language. It is estimated that the tax loss to the Treasury would be about $26.9 billion between 1981 and 1990.

"It is true they see this as a foot in the door," said Robert McIntyre of the Tex Reform Research Group. "They'll come back for more next time. We hope the House conferees will stand firm, because this is just a lousy way to legislate."

The banking groups are hoping just as fervently that the House conferees cave in.

And for this fight, they are going all out. The American Bankers Association, in a special-alert letter to members, urges aiming a blizzard of mail at the conferees.

"Sen. Bentsen suggests . . . that you consider requesting the employes of your bank on their own letterhead to write their senators and representatives in support of the Bentsen amendment," wrote ABA's Gerald M. Lowrie.

Other lenders have followed suit. The National Savings and Loan League, also quoting Bentsen, called for letters from S&L executives, employes and customers. Similar appeals have gone to members of the Independent Bankers Association of America, the U.S. League of Savings Associations and the National Association of Mutual Savings Banks.

"There is unanimity on this and we have pulled the stops," said the Independent Bankers' Ken Gunther. "We all agree something has to be done to help small savers.