"It's difficult to imagine the death of an American politician being met with similar protests," sniffed one recent news report on ABC News.

The funeral of Margaret Thatcher is proving to be one of the few events where British culture appears less formal and less respectful than the usually independent-spirited United States. Thatcher is not viewed as a divisive figure on this side of the Atlantic.

Across the political aisle, she is thought of firmly in the context of her partnership with Ronald Reagan during the cold war, seen as a stalwart part of the patriotic double act that helped to bring about the collapse of the Soviet Union.

Her reputation basks in being part of the warm afterglow of Reagan's presidency – where Democrats and Republicans alike see the 1980s as a sort of highwater mark of muscular Americanism at home and abroad. Certainly Thatcher's domestic policies are either little known or positively portrayed as being part of an effort that "saved" Britain from the threat of socialism – an ideology that is anathema to both of America's political parties.

Thus many Americans have been baffled at some of the critical reaction and coverage of her death in Britain, especially given her status as the first woman prime minister in the United Kingdom's history. Barack Obama himself, echoing words once used about Hillary Clinton's 2008 bid for the White House, portrayed her as "…an example to our daughters that there is no glass ceiling that can't be shattered".

Even Donna Brazile, a top Democrat strategist and a key ally of the Clintons, was generous in her praise. "Margaret Thatcher was tough, decisive and fearless," she said.

But that was nothing compared with the outpouring of grief on the right from all levels of US politics from ordinary Republican congressman to former Alaska governor Sarah Palin.

"We have lost an amazing leader," said South Carolina governor Nikki Haley. Palin said she was "deeply saddened" and lavished praise on her: "Her lessons to all of us will live on forever. She was a trailblazer like no other. We lost an icon, but her legacy, as solid as iron, will live on in perpetuity."

Indeed, the usually fractious American right, which is engaged in a fierce civil war over its future direction, displayed a currently rare united front in the wake of Thatcher's death. The one thing that all rightwing Republicans could agree on was looking backwards in time and seeing Thatcher as a sort of heroic figure of a Golden Age.

When it comes to actually attending her funeral, the response has been patchy. The Obamas may not be attending, but Newt Gingrich, the former House Speaker and resolutely unapologetic free market conservative, is. Representatives of Ronald Reagan's family will attend but it will not be Nancy Reagan, who is "heartbroken" but too ill to make the long journey.

Also unable to come will be both presidents George HW and George W Bush. Reportedly all living American presidents have been invited, but it is not clear that any of them will come. However, one possible future president might show up. The weight of being America's top presence at the funeral at the moment appears to be falling on the shoulders of former First Lady and ex-secretary of state Hillary Clinton, whose attendance has been confirmed.

Clinton, whose period in Obama's cabinet prepared her expertly for the high affairs of state of a foreign nation, will be used to the ceremony of the occasion. But she may still be unprepared for the bitterly split attitudes towards the most high-profile funeral of a British politician in recent times.

• This article was amended on 26 April 2013. Nikki Haley is governor of South Carolina, not North Carolina.