Washington — The rapidly worsening Falklands crisis, says a senior US official, has ''become much more serious than was thought likely'' and appears to be ''on the road toward a more generalized conflict.''
Both Argentina and Britain reportedly are considering what the State Department calls ''minor adjustments'' to US peace proposals made earlier by Secretary of State Alexander Haig.
There was no indication, however, that these adjustments would suffice to break the deepening deadlock between the two contending powers.
The latest word from Argentina was that Mr. Haig's mediation mission was ''suspended,'' following Britain's recapture of South Georgia Island.
A major sticking point that obstructed the Haig mission, says White House adviser Norman Bailey, was how to obtain the views of the 1,800 Falkland Islanders without humiliating Argentina.
Prime Minister Margaret Thatcher insisted that the islanders be asked whether they wished to live under British or Argentine sovereignty in the future.
Buenos Aires, fearing a massive rejection of Argentine rule in such a plebiscite, sought a formula that would phrase the question less bluntly.
How to phrase this key self-determination question still eludes negotiators, according to Mr. Bailey, a deputy to National Security Adviser William P. Clark.
Also in dispute but capable of solution, in Bailey's view, are details of the interim period of administration of the islands, during which ultimate sovereignty would be worked out.
Among other disclosures made by the White House official in a wide-ranging breakfast session with reporters:
* Mrs. Thatcher asked for US mediation after President Reagan, in a telephone talk with President Leopoldo Galtieri, failed to dissuade Argentina from invading the Falklands.
Secretary Haig, it was said, did not volunteer for the mission which propelled him into an arduous transatlantic shuttle between London, Buenos Aires , and Washington.
* The Thatcher government complied with a US request that the British fleet be slowed down en route to the Falklands, to give Haig's mediation more time to work.
Even now, said Mr. Bailey, the British armada ''is not going full speed, but is not dead in the water.''
Bailey confirmed that the Soviets, using surveillance by satellite, aircraft, and trawler, are giving Argentina information on British fleet locations. The US , he said, supplies similar intelligence to Britain.
In the event of war, US officials agree, the United States would side with Britain. Possible measures beyond the refueling of British ships and aircraft are under study in Washington.
The Organization of American States (OAS), meanwhile, resolved in Washington to recognize Argentine sovereignty over the Falklands, but said nothing about sanctions against Britain.
The vote at the special foreign ministers' meeting of the OAS, called at Argentine request, was 17 to 0 in favor, with four abstentions - the US, Chile, Colombia, and Trinidad-Tobago.
US officials, who had lobbied successfully to head off a sanctions vote, regard the resolution as one-sidedly in favor of Argentina and damaging to US mediation efforts. Argentina's leaders were unhappy with the OAS, too, since they had hoped for even stronger support from the organization.
The OAS accepts Argentina's ''right of sovereignty'' over the Falklands, deplores the invocation by Common Market members of economic sanctions against Argentina, and calls for an ''immediate truce'' between Britain and Argentina.
The US bases its diplomacy on UN Security Council Resolution 502, which calls for an immediate ceasefire, withdrawal of Argentine troops from the Falklands, and negotiations on sovereignty.
Implicit in the UN resolution is the assertion that Argentina, not Britain, is the aggressor, because of its April 2 invasion of the Falklands.
The US vote in the Security Council, said Bailey, coupled with abstention from the OAS resolution, effectively incline the United States toward Britain.
He noted, as Prime Minister Thatcher had done earlier, the dangers of mounting a British military operation in the approaching winter weather of the South Atlantic, where high winds and heavy seas prevail.
Argentina, said Bailey, is not a ''banana republic,'' and he cited the discipline of Argentine troops during their occupation of the Falklands. They had refrained from firing at British marines, even when taking casualties themselves.
Still to be measured, as the Falklands drama unfolds, is the damage to US relations with Latin American nations, most of which regard the US as a partisan of Britain.