The Carter administration acted yesterday to dampen over-enthusiastic hopes for a rapid expansion of trade with the People's Republic of China.

At a special State Department briefing with hundreds of businessmen, Treasury Secretary W. Michael Blumenthal and Commerce Secretary Juanita Kreps each stressed in prepared remarks the need to be "realistic."

But they drove the point home with their emphasis in answers to specific questions from the businessmen, who also showed a degree of skepticism on China's ability to finance the enlarged volume of exports the P.R.C. is seeking.

The session -- also addressed by Secretary of State Cyrus Vance, Assistant Secretary for Far Eastern Affairs Richard Holbrooke and presidential assistant Zbigniew Brezinski -- was arranged to explain the reasons for normalization of relations with the P.R.C. and to assure the business community that commercial relationships with the Republic of China (Taiwan) would go on as before.

But the dialogue between the Cabinet officials and the businessmen quickly focused on the legal impediments to an expanded trade with the P.R.C., and the candid admission by administration officials that they don't have full answers to many key questions.

They hope some of these will be resolved later this month when Vice Chairman Teng Hsaio-ping visits Washington, and when Blumenthal and Kreps lead separate missions to China.

Blumenthal warned not only that the Chinese goals for modernization are "ambitious" but that the U.S. is getting off "to a late start in this game."

And in response to a question, he agreed that the "overriding" problem -- and "one that only the Government of China can answer" -- is how the P.R.C. will be able to finance imports of up to $85 billion in capital equipment and technology by 1985.

He later added that "if anyone thinks that our economic relations with China are to be based on a massive extension of (government) credits, I would assure you that that is not our intention.

Kreps listed a number of "hurdles" before the U.S. export potential to China can be realized. She estimated exports could total $10 billion over the next five years.

These obstacles include the present prohibition on Export-Import Bank credits and most-favored nation (MFN) tariff status for China. Extension of these advantages, now enjoyed by Taiwan, will require the settlement of the counter financial claims that the U.S. and the P.R.C. have against each other dating back to 1950, and the negotiation of a bilateral trade agreement.

A California banker wondered whether P.R.C. assets in the U.S. would be protected as trade expands from suits by U.S. citizens who might try to seize them to satisfy the old claims. Holbrooke said this question is "under intensive study, but I think the P.R.C. will be able to operate (here) within certain limits."