Two of President Carter's newest Cabinet members, Treasury Secretary G. William Miller and Energy Secretary Charles Duncan, yesterday vigorously defended Carter's record and predicted he would be nominated and reelected because of his accomplishments.

Miller and Duncan, at a breakfast meeting with reporters, ticked off 10 controversial subjects on which Carter has acted ranging from the economy and energy to the SALT package. "The hard, difficult issues have not been ducked," Miller declared. "They've been presented. And in almost every case, they have resulted in success."

"I can't imagine, with the great challenges this president has taken on, who could have been more successful against all odds," Miler continued.

In spite of the president's low standing in the polls -- only 19 percent of persons asked in a recent Associated Press-NBC Poll gave Carter an excellent or a good rating -- Miller said that Carter's nomination and reelection "is not a question of 'come back.'"

"I believe that if you look at institutions today," he explained, "they are held in low esteem by the American people because of the difficulties of 15 years . . . But when it comes to a decision in the polling place, it isn't the institution's popularity, it is one person against another person.

"And, in this regard, against other choices, the president will be nominated and will be elected," Miller asserted.

Miller and Duncan were responding to questions about whether Carter could defeat a challenge for the presidential nomination from Sen. Edward M. Kennedy (D-Mass.), particularly if the economy does not improve soon.

Even though the economy is in a recession, prices are rising 1 percent a month, and Miller himself is forecasting that unemployment will rise to about 7 1/2 percent by the end of next year from the current 6 percent, the treasury secretary rated Carter's economic policies a success.

In the year and a half since he came to Washington, Miller said, "I have seen the progressive development of a very comprehensive strategy, an integrated strategy to deal with economic problems. Assembling that strategy is difficult because it does challenge the perceived self-interest of different constituencies . . . "

Those policies include "a new attitude on fiscal discipline, an effort to control federal spending and to reduce deficits, to reduce the percentage of GNP represented by federal expenditures . . . " he said.

Duncan, who explicitly endorsed Miller's remarks, added, "If there is anything you see in interagency meetings, it is that the president is making an enormous effort . . . to control spending . . . "

Carter's voluntary wage and price program, Miller said, "has been effective, in my opinion, in holding wages and prices below what they otherwise would have been . . . It has received much attention and criticism, but the fact is, it has been effective."

On energy, Miller said, Carter "has pursued, throughout his administration, the effort to reduce our dependence on oil as a source of energy [and] to reduce our dependence on imported oil . . . He succeeded in moving on natural gas . . . Now he is moving as rapidly as he can . . . to deal with the oil situation."

Another accomplishment, the former Federal Reserve Board chairman added, was the package of actions last November to shore up the dollar, which "has been successful. The dollar is 5 percent higher today on a trade-weighted basis than it was [last] Oct. 31," he said.

Duncan pointed to Carter's effort to increase defense spending. "He has caused that not only in the United States, but also in NATO," he said.

The new energy secretary, who until recently was deputy secretary of defense, added that Carter "has been willing to bite the bullet to do things," mentioning civil service revision and Social Security legislation as two more examples.

Both men also mentioned the president's drive to reduce government regulation of business. To his list, Miller added ratification of the Panama Canal treaties, "being the intermediary to accomplish the Middle East treaty . . . and tackling the hard issues like SALT, which I think will prevail.

"I could go on and on," Miller declared. "I think there is a complete misunderstanding in trying to judge the progress of the nation by beauty contests. Judge the progress of the nation by the substantive accomplishments of the administration."

As for election year economic policies, Miller concluded, "The president will be reelected because he will be perceived to have the courage, the will and the determination to impose . . . policies that are difficult, which require austerity . . . The president who runs on false promises will be nothing but a demagogue. This president will run on substance."