Secretary of State Alexander M. Haig Jr.'s battered efforts to secure a political settlement of the Falklands crisis may now be entering waters every bit as rough and cold as those around the islands themselves.
Argentine sources indicate that Mr. Haig's latest offer to fly here again in search of some common ground between Argentina and Britain - and perhaps to present new United States proposals in the Falklands dispute - has been torpedoed.
The Argentines ask: Why make the trip? If Mr. Haig has anything new to propose, they say, he can do so to Foreign Minister Nicanor Costa Mendez, who is in Washington leading Argentine efforts to curry hemisphere support for a possible invocation of the Rio de Janeiro Treaty of Mutual Assistance in the Falklands dispute.
If there is indeed a new Washington proposal, some Argentines suggest it probably involves temporary US rule of the Falklands until the dispute can be sorted out.
Such a proposal appears unacceptable to Argentina - at least for the moment. But the increasing likelihood of a British landing on the Falklands, which could result in the pulling down of the Argentine flag, may make Argentina more receptive to the proposal.
For now Argentina appears most intent on winning Latin American support for any decision to invoke the Rio de Janeiro treaty, challenging the British as aggressors in the Falklands dispute.
Moreover, Argentina in effect has decided that US mediation of the Falklands dispute - centered on the Haig shuttle diplomacy between London and Buenos Aires - is clearly wasted effort.
There is speculation here that Washington's reported last-ditch proposal to stave off war in the Falklands has probably come too late for the British as well. There are growing indications that Britain is on the verge of landing troops on the Falklands if it has not done so already, as a follow-up to its reoccupation of the South Georgia Islands April 24.
Rear Adm. Sandy Woodward, commander of the British naval armada now in the South Atlantic, termed the South Georgia landing ''the appetizer. Now comes the strong blow,'' a clear reference to the Falklands.
But Argentina officially continues to bank on hemisphere support in the event of a British landing on the Falklands.
Whether such hemisphere backing will be forthcoming, however, remains problematic. Argentina is beginning to suspect this. And there is growing pessimism here for the prospect of many Latin American countries offering troops or other aid to Argentina.
Latin America's biggest nation, Brazil, is a case in point. Over the weekend top Brazilian officials gave every indication of doing their best to ignore the Argentine calls.
The Argentine public has not been told the full story of the British recapture of the South Georgias. The media here suggest that Argentine resistance continues.
The British have a different version of what happened. They claim to have captured close to 200 Argentine Navy and Army personnel. The British naval commander of this operation also has reported that he entertained the Argentine Army commander on South Georgia and the commander of the Argentine Navy submarine caught in South Georgia's harbor aboard his ship following the British takeover.
But Argentine newspapers, full of stories about continuing Argentine resistance, are also laden with articles suggesting that by landing on South Georgia the British actually have suffered a reverse.
Some observers see this twist in logic as an Argentine effort to put the best light possible on the worsening situation.
Argentina continues to find it inexplicable that Britain decided to send its naval armada to the South Atlantic and possibly even recapture the Falklands. It was widely expected that Britain would do little more than raise a whimper of protest over the Falklands seizure April 2 and the subsequent April 3 takeover of South Georgia.
Yet Argentina is beginning to realize that its seizure of the Falklands has stirred far more than a hornet's nest of opposition.
Where the Argentine public stands on thisis hard to determine. A labor demonstration April 26 in the Plaza de Mayo in front of the Casa Rosada, the Argentine White House, suggested there could be growing opposition to the military government here.
Placards favoring the Falklands occupation by Argentina were accompanied by shouts of ''Down with dictatorship.'' A loss of the Falklands to the British could make it difficult for Army Gen. Leopoldo Fortunato Galtieri's government to survive.