President Carter's supporters today engineered a set of rules that virtually assure the president safe passage across the political shoals of the Democratic midterm conference.

The rules for the conference, which begins here Friday night, will allow liberal dissenters to air their differences with the administration's domestic policies but will all but guarantee defeat of any resolution that lacks White House approval.

With winter storms in the Midwest and West hampering delegates headed here for the mini-convention, Democratic National Chairman John C. White gained quick approval from the party's executive committee for procedures designed to protect Carter from any embarrassments during the three-day meeting.

The key decision was a 13-to-7 executive committee vote requiring a majority of all 1,633 elected delegates -- and not just a majority of those present and voting -- for approval of any resolution at Sunday's closing convention session.

With bad weather and apathy combining to keep a significant number of delegates home, and others planning to leave during the day Sunday for their return trips, the odds are very heavy against there being 817 votes for any of four mildly dissenting resolutions that will be brought up for debate.

Nonetheless, party liberals tonight began circulating a resolution that represented a major challenge to Carter administration proposals to reduce spending on social programs in next year's budget.

Declaring that these cuts "may well result in a recession and rising unemployment," the resolution, drawn up by leaders of the party's liberal wing, urged that these programs be funded at least at current levels in the fiscal 1980 budget.

At a caucus that attracted more than 600 persons -- not all of them delegates -- they also voted to press for adoption of convention rules on Friday, a move that appeared doomed to failure. Currently, those rules are not scheduled for discussion until Sunday.

A tightly controlled, even dull convention would suit the White House just fine, although presidential aides have been predicting a series of "lively debates" during the proceedings.

The president leaves for Memphis Friday afternoon intent on convincing the assembled Democrats that his stringent domestic economic policies and other anti-inflation measures do not nean an abandonment of traditional Democratic social welfare goals.

The reception his keynote speech to the convention receives Friday night will be an important measure of how well that message, which he has been preaching for weeks, is going over with the party.

"It will be a difficult reconciliation of the traditional goals of the party and the changing economic and political realities of the situation," one White House official said. "I think he will try to say there is a difference between someone who takes these steps because he doesn't believe in government or that government should not be in these kinds of programs, and to be for these unpleasant steps because they are the most practical way to go about it."

The aide added: "Gradually, painfully, the party has to make adjustments to accommodate itself to the changing times. It has in the past and has maintained its vision, and this is another time that calls for that kind of assessment."

A test of that flexibility might come on the issue of national health insurance. One minority resolution calls for enactment of it as promised in the 1976 Democratic platform. The White House is supporting an alternative resolution reaffirming the commitment but without any timetable.

The other dissenting resolutions on inflation, energy and agriculture lambaste "hard-money policies," the power of multinational and energy corporations, natural gas deregulation and "the idea that we can fight inflation with joblessness and the misery of a recession." The White House-backed alternatives basically endorse the outlines of current Carter policies in these fields.

A group of left-wing labor and liberal Democrats, calling itself the Democratic Agenda, collected more than 450 delegate signatures on petitions to bring the dissident resolutions before the mini-convention.

But leaders of the group conceded that they will have an uphill fight to get another 360 delegates on the floor Sunday to vote for them, in preference to the administration-backed resolution that came out of a committee handpicked by White for the job.

In an elaborate display of courtesy to the dissidents, White recommended today -- and the executive committee approved -- a procedure that will guarantee a series of direct test votes Sunday between the official and dissident versions of the resolutions on health care, inflation, energy and agriculture.

Dan Horgan, executive director of the Democratic National Committee, said his head count of the delegations convinced him "it won't be close" on any of the four resolutions -- or on a preliminary test vote which White has invited on the question of what constitutes a majority in the mini-convention.

Rep. Donald M. Fraser (D-Minn.), a leader of the liberal forces, told the executive committee this morning that his group wanted a "workable conference" and was prepared to accept the procedures White offered.

The accommodating attitude taken by Fraser -- who was defeated for nomination to the Senate last September after giving up his safe House seat -- is but one of a series of signposts of a structured harmony at the meeting, which Carter aides had previously anticipated with some apprehension.

Earlier, the White House negotiated an agreement with Sen. Edward M. Kennedy (D-Mass.) and United Auto Workers President Douglas Fraser on the issue of health insurance.

The two men have publicly opposed Carter's decision to delay a start on the program until the budget deficit and inflation have been reduced.

But they agreed to the generalized wording of the official health resolution, simply reaffirming the 1976 platform without a starting date.

So secure was the administration's control of proceedings that some officials began predicting that there would be further voluntary concessions to the liberal dissidents -- perhaps a rewording of the inflation resolution.

Detroit Mayor Coleman Young, a Carter ally who voted with White on the rules test, said he was drafting new language that would let the miniconvention express the sentiment that budget-cutting measures "not be at the expense of the poor and the minorities and the cities they live in. We want to say that they should not be the sacrifical lambs in the war on inflation."

The mini-convention, mandated by the 1976 Democratic convention, opens formally Friday night with speeches by Carter, House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) and others.

Saturday is given over to issue panels on two dozen topics, and Sunday is the voting day for resolutions.

The president is expected to attend workshops on defense policy and arms control and on the economy and inflation before returning to Washington Saturday, well before any of the debates over resolutions.

Vice President Mondale will also attend some of the workshops, and is to address the convention Sunday. Mondale has also scheduled a series of private meetings in Memphis with labor officials, blacks and liberals who are the most upset with the conservative direction of Carter's domestic policies.

Six months ago, with the president's standing in the polls continuing to slide, White House officials feared that the midterm conference could produce a major political embarrassment to the administration. That fear evaporated with Carter's political resurgence, but the White House nonetheless has taken elaborate steps to assure maximum tranquility at the conference.