Opinion polls show her Social Democrats are headed for their weakest result since before World War II: many Danes blame Frederiksen for not doing enough to protect their Nordic welfare model, while others point to growing weariness after nearly seven years of her leadership.
Frederiksen, 48, called the vote months before an October deadline, in what observers said was an effort to capitalise on an uptick in popularity when Trump's rhetoric about controlling Greenland intensified in January and he refused to rule out military force.
But the Greenland issue has since moved to a less heated diplomatic track and has been overtaken by domestic concerns including a proposal for a wealth tax and debates about immigration.
Still, Frederiksen has campaigned on a promise that her tough and tested leadership skills will help the Nordic nation of six million navigate a complex relationship with Washington and a European response to Russia's war with Ukraine.
"I know that sometimes I express myself a bit bluntly," she said during a recent campaign event. "But given the times we live in, it is perhaps very good that there are some things that cannot be misunderstood: that Russia should not be allowed to win or that Greenland is not for sale."
Frederiksen, who has led Denmark since 2019, was the first premier to bridge the left-right divide in Denmark in more than 40 years, but her coalition is now projected to lose its parliamentary majority.
"To a large degree, this election is about Mette Frederiksen," said political analyst Hans Engell, adding that, while some voters view her as the right person at a time of crisis, others see her as too authoritarian.
Her Social Democrats, whose tough asylum reforms had alienated some on the left, have recovered in polls since the Greenland crisis, rising from a December low of 17 per cent to around 21 per cent.
But the left-leaning bloc is still expected to fall short of the 90 seats needed for a majority in Denmark's 179-seat Folketing, with projections pointing to around 85 seats.
With left-wing allies expected to hold firm and the right bloc fractured, however, she remains the favourite to form the next government as parties reposition themselves along more traditional left-right lines.
In Denmark's parliamentary system a government need not command a majority - it simply must not have one against it. The right-leaning bloc is led by Defence Minister Troels Lund Poulsen of the Liberal Party, while the outcome could hinge on former prime minister Lars Lokke Rasmussen, leader of the centrist Moderates and current foreign minister, who is positioned to play kingmaker.
Polls close at 5am on Wednesday AEDT.
