The President of the European Council is detested in his native eurosceptic Poland, a major Brexit ally, and is seen as a toxic figure.
EU leaders will meet in Brussels tomorrow and are expected to extend Mr Tusk’s term as Council president for another 30 months despite Polish efforts to oust him.
The country’s ruling right-wing Law and Justice party (PiS) has accused former prime minister Mr Tusk of betraying his nation by condemning Poland's free speech record.
Theresa May has a tough decision to make tomorrow at a meeting of the European Council
To exacerbate matters, Jaroslaw Kaczynski, the leader of Poland’s ruling party, also holds Mr Tusk “morally responsible” for his brother’s death.
Then-president Lech Kaczynski died in a plane crash while Mr Tusk was prime minister, with investigators blaming pilot error.
Now, instead of rubber-stamping Mr Tusk’s second term, PiS has called on EU leaders to support their candidate Jacek Saryusz-Wolski as the new Council president over Mr Tusk.
Donald Tusk is popular among europhiles but detested in his native Poland
The Prime Minister has become embroiled in the row just weeks before she is expected to trigger Article 50.
Theresa May could choose to butter EU leaders up ahead of the crucial Brexit negotiations by supporting the preferred candidate Mr Tusk.
But the PM risks alienating Poland, a major Brexit ally, if she does not support their candidate.
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One EU diplomat, speaking anonymously, described the situation as a “lose-lose situation” for Mrs May.
He said: “Either Mrs May alienates almost all the other member states or she upsets the Poles, who she’s spent months and months cultivating.
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EU leaders will meet tomorrow to rubber-stamp an extension to Donald Tusk's reign
Theresa May just can’t win. It’s a lose-lose situation for Britain
European Union official
“She just can’t win. It’s a lose-lose situation for Britain.”
Witold Waszczykowski, Poland’s foreign minister, said: “Saryusz-Wolski will be better for Brexit negotiations."
Polish Prime Minister Beata Szydlo said: “We cannot allow the creation of such a dangerous precedent whereby a democratically-elected government in a member state comes under political attack from the president of the European Council.”
Refusing to bow to pressure, Number 10 indicated Mrs May had no intention to back the plot to remove Mr Tusk.
Jacek Saryusz-Wolski is Poland's preferred candidate for the presidency
A Downing Street spokesman said: “The Prime Minister has been clear that she thinks [Tusk] is doing a good job.”
Mr Tusk’s first term is due to end in May and he declared his candidacy in early February.