The 20 members of the Senate Finance Committee knew something was up when each of them received a letter from his alma mater, begging him to change a provision in the House-passed tax-revision bill.

The subject was an issue, like so many in tax revision, that is little known to the general public but of desperate concern to those directly affected. More than a month before members of the committee are to begin writing their tax legislation, lobbying on the contributions provision is just one of hundreds of little dramas playing on the stage of tax overhaul.

The struggle is a microcosm of almost all the contradictions inherent in the attempt to make the tax code fairer and more efficient. It juxtaposes tax breaks for millionaires against the importance of large gifts to charity; a tax system where everyone must pay a fair share against one that provides incentives for purposes deemed worthwhile.

The lobbying campaign features the entire Ivy League, as well as many other universities and a panoply of foundations, hospitals, museums and symphony orchestras. Members of a hastily assembled coalition of 30 organizations have already met with each member of the Finance panel, some more than once, during the few weeks Congress has been in session this year and have deluged senatorial offices with letters and phone calls.

"Just start calling private colleges," said an aide to a Finance member when asked what institutions are active in the battle. "We've heard from every one of them."

Yet the tax change in the House legislation would directly affect only a relative handful of super-rich taxpayers, perhaps 200,000. It passed in the House Ways and Means Committee with little public attention as a watered-down modification of President Reagan's tax-overhaul proposal. And it is far weaker than the limitations proposed in the original Treasury Department plan.

The details are complex, but the effect is simple: The provision would reduce the tax deduction available to many wealthy taxpayers who donate to charities property that has increased in value.

Now, if an individual sells shares of stock that originally cost, say, $400,000 and are worth $1 million, he would have to pay taxes on the $600,000 in "appreciation." If he gives the stock to a university or other charity, however, he can deduct the full $1 million from his income on his tax form, reducing his tax liability. The $600,000 in appreciation is never taxed.

The Treasury's proposal would have limited the possible tax deduction to the original cost of the appreciated property, $400,000 in the example, plus an additional amount to account for inflation. But loud protests from charities, including personal appeals to Reagan, led the administration to weaken the change in the proposal sent to Congress.

The revised version would limit the deduction only for purposes of the minimum tax, the alternative tax system designed to ensure that wealthy individuals do not escape taxation.

Under the House bill, if a taxpayer has so many deductions and credits that he would pay little tax, he must recalculate his tax under the minimum system, which limits the use of certain deductions so that the taxpayer's taxable income is larger. That expanded income is taxed at a flat 25 percent rate.

One of the deductions that would be limited is the one for appreciated property. The effect would be to deny all or part of the deduction to taxpayers covered by the minimum tax, especially those who make extensive use of other tax breaks.

Because the House bill would greatly expand coverage of the minimum tax from its current small scale, giving would become more expensive for almost every big-ticket donor, opponents of the change argue. They estimate that charitable donations would be cut $600 million to $1 billion per year.

"In this country it's been our tradition to do a lot of things in the private sector that in other places are done in the public sector," said Benno C. Schmidt, a New York venture capitalist who is board chairman of Memorial Sloan-Kettering Cancer Center. "One of the ways we have done that is by allowing the deduction. You just don't want to knock out the support of those institutions on which this country relies in a very large measure for its claim on excellence."

Schmidt, a member of the advisory board for the coalition lobbying on the issue, said he has spoken or written to every member of the Finance Committee and the House Ways and Means Committee about it. So have dozens of college presidents, many of whom descended on senatorial offices during a convention here two weeks ago.

"Very few senators come from a state without a university," said Sen. Daniel Patrick Moynihan (D-N.Y.), who strongly favors retaining the deduction.

The coalition, called the Alliance for Philanthropy, was the brainchild of Washington lobbyist Dan Flanagan, whose clients include Sloan-Kettering. After the House bill passed, Flanagan said, alarmed proponents of the deduction realized their strategy had been flawed: "We were making our case to staff and by the time the opportunity presented itself, it was part of the minimum tax," he said.

This time around, coalition members decided, they would seek to persuade senators themselves. At weekly meetings, they allocate their resources among Senate Finance members, so that each one will be contacted by influential charitable groups from his own state.

At one recent pow-wow, for example, two Oregon colleges, a foundation, the Oregon Symphony Orchestra and a public-land trust agreed to talk to Finance Committee Chairman Bob Packwood (R-Ore.). Sen. John Heinz (R-Pa.) would hear from the University of Pennsylvania, the local United Way, a community foundation and an area museum group. The University of Minnesota was to call Sen. David F. Durenberger (R-Minn.). Sen. William L. Armstrong (R-Colo.) would hear from the Colorado Open Lands Foundation, and ranking committee Democrat Russell B. Long (D-La.) from the president of Tulane University and the New Orleans Symphony. And so on.

No such lobbying is taking place on the other side of the issue. The only support for the provision comes from tax-policy experts who point out that the appreciated-property provision is like almost no other section of the tax code in that it gives taxpayers a double benefit: They can not only avoid taxation on the property's increase in value, but they can use that higher value to shelter income from other sources.

The deduction "conflicts with basic principles governing the measurement of income, produces an artificial incentive to donate appreciated property rather than cash and also leads to abuse and administrative problems for the Internal Revenue Service when taxpayers overvalue donated property," according to the Treasury Department's original tax plan.

"Here is someone giving something worth $30,000. They get a $100,000 donation and the Treasury does not get the tax revenue, and that's not the way it's supposed to work," said Sen. Bill Bradley (D-N.J.), a Finance member.

Proponents of the deduction marshal a host of arguments against such objections, contending that most appreciated gifts are stocks or real estate, which are fairly easy to put a price tag on.

Those arguments and others seem to be making headway with the Finance Committee. At a hearing on the minimum tax, several senators made a point of objecting to including appreciated property.

There is little sign the House-passed provision will be in the draft tax-overhaul legislation Packwood is preparing to offer to the committee. During a meeting last week of aides to senators on the Finance panel, staffers were asked if their bosses objected to the provision. Hands shot up around the room.