Faced with his own deepening political problems, President Carter recalled tonight another embattled Democratic president's warning that fear of an uncertain future must not paralyze the nation's ability to deal with its most pressing problems.

In a speech delivered to a Democratic Party fund-raising dinner here, Carter echoed Franklin D. Roosevelt's Depression-era declaration - "The only thing we have to fear is fear itself" - and sought to apply that lesson to the most serious problems afflicting his adminstration.

"One of the most immoblizing fears in our nation today is the fear of being misled and cheated," the president said of public skepticism about the causes of the energy shortage. "As much as anything else, this keeps our people from conserving energy and doing our part to hold down inflation. I believe Americans are willing to do their part as long as they feel everyone else will."

"In the long run," he declared, "we will all suffer if we delay and dally in the mistaken belief that our problems will miraculously disappear. The choice is between temporary inconvenience now or real hardship later."

The president flew here from Camp David, Md., where he spent Friday night and most of today with some 10 House Democrats and their spouses in an effort to begin patching up his relations with Congress.

One of those at Camp David, House Democratic Whip John Brademas of Indiana, said the sessions touched on energy, inflation, unemployment, implementation of the Panama Canal treaties, and changes in the makeup and behavior of the House.

Although refusing to supply details, Brademas called the overnight gathering "free-wheeling, unconstructed. It was a genuine two-way dialogue. It was a very instructive weekend. It was not a hard-sell weekend."

Scarcely any crowds turned out here to see the president, but he was warmly received by about 3,000 at the dinner.

In his speech to the Indiana Democrats, he defended his decision to order a gradual decontrol of domestic oil prices and warned of the consequences should the Senate reject the new strategic arms limitation treaty (SALT) with the Soviet Union. Carter also delivered a milder version of his address to the Democratic National Committee last week, in which he chided the Democratic-controlled Congress for refecting his energy proposals and other domestic legislation.

But his main theme tonight, with its echo of Roosevely confronting the worst economic conditions in the country's history, was an attempt at a Roosevelt-style uplifting sermon on the problems of the day.

"Our land is broad, our people diverse, and many are frightened by a future they see as very different from the past we have known," the president said. "It will be very different just as our world is very different from that of our ancestors, but this should not be a cause of fear. The problems are real and they are serious, but they are manageable if we have the courage and the will to face them together. There is no doubt that we have the strength."

"We cannot let all that strength, all the innate power of our natural and human resources, be frittered away in fear and futility. Franklin Roosevelt understood how fear can immobilize people, and in a much more desperate moment he warned us of the power of fear to destroy. We cannot let fear of change, of uncertainty or the fear of some manageable limit on material goods immobilize our mighty nation."

The president's warning about fear was clearly directed at Congress, and beyond it a public that White House aides increasingly complain is immobliized by a refusal to accept the energy shortage as real.

Citing his party's control of Congress and the executive branch, Carter said the American people "did not give us majorities so we could vote down every solution offered, complaining that they were not perfect. There are no perfect solutions, but I believe that the people are willing to follow us if we meet our responsibilities and devise the best solutions we can."

Of his most controversial energy policy decision, the one that has greatly intensified criticism of him and widened the White House estrangement with Capitol Hill, the president said:

"There will be strong pressures in the coming weeks to continue government controls on oil. As you know, the controls are not working. You have seen what has happened to prices. These controls encourage waste, discourage production of oil in the United States and subsidize oil imports.

"We are in this mess today in part because we insisted too long on that course . . . the message must be clear to all Americans - we cannot continue to increase our use of oil and gasoline in the face of reduced supplies.

Carter devoted the bulk of his speech to domestic issues, particularly for him a standard appeal for support for the SALT II agreement. After seven years of negotiations, he said Senate rejection of the agreement would mean that "the process of conenergy, but included what has become trolling nuclear weapons would be difficult to resurrect." CAPTION: Picture, President Carter and Sen. Birch Bayh join at Democratic dinner in Indianapolis. AP