The Republican Party yesterday began a week-long series of ripostes to President Carter's State of the Union message, saying Tuesday's speech chasing dollar at home and our prestige and influence abroad."

In the closing session of the Republican National Committee's midwinter meeting here, GOP leaders said that Carter's anti-inflation budget is "by no means tight enough" and his foreign policy reflects a "strangely detached view" of America's role in the world.

But the GOP critics -- party chairman Bill Brock, former White House economic adviser Alan Greenspan and former disarmament negotiator Fred Ikle -- all conceded there was a more-than-faintly-Republican tone to Carter's messages to Congress this week.

"The State of the Union [address] and the budget... were as Republican as I can imagine," Greenspan said, and Brock added that "the president is saying some of the right things."

The "right things," as the Republicans saw it, were Carter's insistence on reducing the federal deficit and his pledge to increase defense spending in fiscal 1980. But on neither point, according to the speakers yesterday, did the president go far enough.

Yesterday's panel session was the opening of a series of Republican rebuttals to Carter's nationally televised speech Tuesday. The party asked all three networks for equal time to reply, and ended up with three half-hour periods over the next week.

Last night, four GOP congressional leaders got their chance on NBC-TV. Saturday at 10:30 p.m., six newly elected Republicans will discuss the president's message on ABC-TV. And Tuesday at 8 p.m., CBS-TV will broadcast a "town meeting" in which four ranking Republicans will answer questions from an audience in Frederick, Md.

At the national committee session yesterday, Greenspan, who headed the Council of Economic Advisers in the Ford administration, said Carter's prescription for reducing inflation "has a relatively low possibility of coming out right."

He warned that results could be disastrous if overseas holders of dollars begin spending them in large amounts in the United States. "If those foreign dollars pour in, then, in effect, we double up the inflationary pressures," Greenspan said.

Ikle, who was director of the Arms Control and Disarmament Agency under Presidents Nixon and Ford, criticized Carter for failing to discuss "our dangerous intelligence failures, not only in Iran but in Afghanistan, where our intelligence failed to see the approaching upheaval."

Referring to Carter's reference Tuesday night to the power of a single Poseidon missile, Ikle asked, "How's that going to stop the Soviets from, say, sending ground troops into Iran?Because their nuclear missiles would probably deter us from using Poseidon in such a case."