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.