The leader of a nation always friendly to the United States has urged his 15 million people to stay up all night to see America beaten.

Australian Prime Minister Bob Hawke has told John Bertrand, skipper of America's Cup challenger Australia II, that all Australians will be up watching and listening for his victory over the yacht Liberty Saturday in the final race of the America's Cup series. And at huge cost, Australian TV networks are taking a direct satellite coverage of the race to feed across Australia throughout the hours Hawke wants his people to watch.

Because of time differences, TV sets and Down Under patriots will be alight from about 2 a.m. to 7 a.m. Sunday morning.

Prime Minister Hawke went one extraordinary step further. He told Bertrand in an official message, "If it gets tight, put out a call and we will all face Newport at once and blow our hearts out."

The message showed that Hawke is not a yachting man. Australia II certainly does not want the gale such a huff would create. But it shows the prime minister knows the people who gave him a landslide election victory in March and who like him even more now, according to opinion polls.

Australia has become hysterical over the possibility that its yachtsmen will take the America's Cup away from the United States. The Down Under media are treating the event off Newport, R.I., as if it were of earth-shaking significance.

Every paper in the country bannered Australia II's latest victory in headlines never less than two inches deep. Sydney's Daily Mirror, one of the local dailies owned by Rupert Murdoch, went as far today as printing its lead headline in red ink. It read: "We're gonna win ya!"

Most Australians, in fact, are not yachtsmen. Ocean and even harbor yacht racing in Australia is the same as it is in the U.S., generally the preserve of the well-to-do. The only difference is the relative size of the fortunes.

But they love the prospect of a victory, especially against their American friends. Not since a couple of teen-agers named Lew Hoad and Ken Rosewall took the Davis Cup away from the United States three decades ago have Australians been as excited about a sporting contest.

Most people in Australia have no idea what they would do or how the country would be affected if Australia II won the New York Yacht Club's ancient silver mug. No more than one in 10 Aussies would know a lee from a luff, and spinnakers are thought of as how the ancient Australian game of two-up (which consists of betting on the toss of two pennies) is started.

But half the population is now convinced, thanks to the NYYC's attempts to declare Australia II illegal, that between now and Sunday breakfast the only way the Australian yacht can lose is if Liberty is permitted to use a motor.