Treasurer Joe Hockey has warned that Hillary Clinton's bid to win the 2016 US presidential election will not be a "lay-down misere" for the Democratic front runner.

Mrs Clinton has officially announced that she is running for the presidency through a video posted on social media.

Mr Hockey, who is currently in New York for a G20 meeting of global finance ministers, said: "Obviously Hillary Clinton is very familiar to the Australian people and, importantly, Australia is very familiar to her.

"I have no doubt she will be a formidable candidate for the Democrats but from what I hear she's not going to have a particularly easy run in either the primary or necessarily in the election and I think Americans on the ground, particularly here in New York, have a view that it's not a lay-down misere for Hillary Clinton," Mr Hockey said.

Assistant Treasurer Josh Frydenberg said: "She is certainly the favourite to win the Democratic nomination and we welcome Hillary Clinton for putting up her hand for the presidential race. She is a good friend of Australia and was certainly one of the architects of the pivot to our part of the world."

But Mr Frydenberg said Mrs Clinton will face a "formidable" set of Republican candidates including former Florida governor Jeb Bush, Florida Senator Marco Rubio, Kentucky Senator Rand Paul and Texas Senator Ted Cruz.

"It will be quite remarkable if another Clinton ends up in the White House; it will mean 24 of the last 32 years in the United States has seen either a Clinton or a Bush in the White House," he told Sky News.

Mr Frydenberg noted that, while the American economy has improved recently, many Americans have been unhappy with Barack Obama's performance as President.

Some senior ministers in the Abbott government were frustrated when President Obama used a major speech during the G20 meeting in Brisbane last year to warn of the dangers Australia faces if the global community doesn't tackle climate change.

Former prime minister John Howard and Mr Obama had a war of words in 2007 over the then US presidential hopeful's plan to bring US troops home from Iraq.

Mr Howard said: "If I were running al-Qaeda in Iraq, I would put a circle around March 2008 and be praying as many times as possible for a victory not only for Obama but also for the Democrats."

Relations between Kevin Rudd and President George Bush suffered a strain when reports emerged claiming that Mr Bush had asked Mr Rudd in a private phone conversation what the G20 was.

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