As the British armada braces itself for a battle in the icy Falkland waters, Margaret Thatcher is faced with the perhaps equally difficult task of keeping public support of her tough stand from flagging.
Until now the British Prime Minister has managed to rally her political critics to the opinion that Argentina's military junta will only retreat from the Falkland Islands at gunpoint. The British public so far has given her overwhelming backing. And the West European allies have also rallied to her side.
However, with the possibility of a long and bloody clash between Argentina and the British fleet nearing by the hour, many analysts here expect political and public opinion to begin to shift.
Already Mrs. Thatcher has been taking fire from all three opposition parties - Labour, the Liberals, and the Social Democrats. She is charged with not searching hard enough for a diplomatic exit from the Falklands crisis.
Such criticism came to a head at a stormy emergency debate in the House of Commons April 29, broadcast nationwide. Labour Party leader Michael Foot assailed the Conservative government for not calling United Nations mediators into the dispute. Mr. Foot urged Mrs. Thatcher to dispatch Foreign Secretary Francis Pym to New York for talks with UN Secretary-General Javier Perez de Cuellar.
Mrs. Thatcher replied, ''If anyone can solve the crisis, it's General (and Secretary of State Alexander) Haig. The United Nations cannot always enforce its judgment.''
Although Mrs. Thatcher in her opening address to Parliament was unwilling to discuss the details of the American peace plan, she declared that it ''inevitably bears the hallmarks of a compromise.''
She added, ''The crisis was started by Argentina invading the Falklands and it can only be settled by an immediate withdrawal of Argentine troops.''