President Carter called on state and local government officials yesterday to adopt their own anti-inflation programs and promised that the federal government will cut program costs by streamlining its system of providing grants to the states and localities.

The president spoke to about 175 state and local officials in the Executive Office Building, asserting once again that he will not "back down" in his attempt to control inflation.

Carter said there were some hopeful signs in the anti-inflation battle, including what he said was gorwing acceptance of the administration's "real wage insurance" proposal. But on Capitol Hill yesterday, Federal Reserve Board Chairman G. William Miller was less optimistic about the anti-inflation prospects.

Miller told the House Banking Committee that he expects inflation this year to exceed the administration's forecast of 7.5 percent, reaching as high as 8.2k percent. He conceded, however, that "we could be fortunate" and hold the inflation rate to the 7.5 percent target.

Private economists generally have been even less optimistic than either Miller or the White House.

The Fed chairman also said that he expects the economy to grow this year by 1.75 percent to 2.25 percent, compared with the administration's forecast of a 2.2 percent growth rate. He said he expects the unemployment rate to hold steady during most of 1979, but to rise toward the end of the year.

White House officials invited state and local officials from around the country to Washington to ask their help in the anti-inflation program. The president had done the same thing in earlier speeches, but this occasion gave the White House an opportunity to publicize the anti-inflation effort.

The state and local officials were given a 30-page booklet explaining the administration's anti-inflation program and asking them to establish their own. Specifically, they were asked to abide by the federal wage and price standards in their dealings, adopt "anti-inflationary procurement policies" by purchasing goods and services only from firms that comply with the standards, improve their regulatory practices and productivity in government services and use tax and budget policies to combat inflation.

Federal officials said they would do their part by streamlining the $80 billion grant-in-aid system. Steps to be taken, they said, would encourage consolidation of grant programs, steam-line planning requirements, limit federally mandated costs and reduce duplication and paperwork.

"If there was ever an issue in which the system of federalism can be tested and in which the system of federalism can be successful if welded together, this is it," Carter told the state and local officials in appealing for their help.

The president said the response of business to the anti-inflation program has been "overwhelmingly good," and that organized labor was becoming "increasingly supportive." He said the "real wage insurance proposal," designed to protect workers from inflation that exceeds the administration's 7 percent wage increase standard, was gaining support in Congress.

"I'm not going to back down," he said of the effort. "I am not going to yield to pressure."