Activist Mitch Snyder yesterday completed the 47th day of a hunger strike aimed at forcing the Reagan administration to respond to the needs of the homeless and he is deteriorating rapidly, according to a doctor who examined him.

Snyder, 41, a member of the Community for Creative Non-Violence and a nationally known advocate for the homeless, said he is prepared to starve himself to death unless federal officials agree to appropriate $5 million to repair the squalid downtown Washington shelter CCNV operates and withdraw a report issued by the Department of Housing and Urban Development that Snyder says greatly underestimates the number of homeless people.

Dr. Deborah B. Goldberg, a Silver Spring internist who examined Snyder at the request of his friends, said yesterday that unless he starts eating "there's a real possibility that in the next week the situation could become critical" because "nobody knows how long he can last."

Goldberg, who is scheduled to reexamine Snyder today, said he is suffering from dehydration caused by diarrhea and bronchitis that cannot be treated because, in his malnourished condition, he cannot tolerate antibiotics.

A visibly weak Snyder, interviewed yesterday as he lay in his bed at CCNV's communal house at 1345 Euclid St. NW, said he "fully expects" the administration to comply with his demands.

"God has called me to do it," said Snyder, who has lost 55 pounds since Sept. 15, when he began fasting and drinking only water. "People's lives are at stake, many more than mine. I don't want to die but there is no better way than this that I could serve the people out on the streets."

Administration officials yesterday said they did not intend to respond to Snyder's demands and urged him publicly -- as several have privately -- to abandon the fast, which has attracted international attention.

"He doesn't have to die," said Dr. Harvey Vieth, chairman of the Federal Task Force on Food and Shelter, who several weeks ago asked Snyder to stop fasting. "He can start eating and continue his campaign for the homeless. It's his call."

Vieth, a high-ranking official of the Department of Health and Human Services, has worked with Snyder since December when the federal government agreed to lease for $1 an abandoned building at 425 Second St. NW for use as an 800-bed shelter for the homeless. The shelter, located in a building once occupied by Federal City College, is one of the largest in the country.

"We are not in a position to do anything about the HUD report," said Vieth. "The only money available is in the Defense Department . . . to appropriate $5 million they would have to declare the shelter a military installation."

This is not the first time Snyder has publicly undertaken a long fast, a fact doctors say may partially account for his rapid deterioration. In 1978, near death, he was rushed to Sibley Memorial Hospital after Georgetown's Holy Trinity Church refused his demand that the church appropriate money for the poor. In 1982, as a result of protests by religious leaders around the country and a 64-day fast by Snyder, the Reagan administration agreed to change the name of an attack submarine from Corpus Christi to City of Corpus Christi. Snyder and others who protested said that naming the submarine Corpus Christi -- Latin for Body of Christ -- would be sacrilegious.

In another development yesterday, eight jurisdictions in the Metropolitan Council of Governments signed an agreement to share shelter space for the homeless during the coming winter and the months beyond.

The memorandum of understanding -- the outgrowth of a COG task force organized in March, 1983 -- provides that when homeless people cannot be accommodated in one jurisdiction they be housed in a neighboring one.

Between 900 and 1,000 beds will be pooled in the housing experiment, according to Scott Riley, a staff member on the COG task force. Only public shelters are covered by the agreement, although private nonprofit shelters will be free to contract for services with any jurisdiction.

Signing the agreement were the District of Columbia, Prince George's, Montgomery, Arlington and Prince William counties, and the cities of Greenbelt, Alexandria and Falls Church.