There is also the uncomfortable issue of Trump's comments about women, some of which he has apologised for
The visit has been presented as a diplomatic coup in Britain, where the idea of the "special relationship" still holds strong, and is being closely watched in Washington as Trump's foreign policy takes shape.
Trump has offered rare support for Brexit among global leaders, seeing parallels with his own election campaign, and saying Britain was "smart" to vote to leave an EU that he believes is now falling apart.
He has also pledged to move quickly on agreeing a trade deal with London -- welcome words for May, who last week conceded publicly for the first time that Britain would be leaving Europe's single market.
But analysts note that Trump's protectionist, "America First" rhetoric appears at odds with May's promise to turn Britain into a free trade champion.
"There is a national sympathy from Trump to this country because of Brexit," said Stephen Burman, professor of American politics at the University of Sussex.
"But to me, 'America First' and a 'Global Britain' are practically contradictory statements.
"That's not going to change because of a trip", he added.
There is also the uncomfortable issue of Trump's comments about women, some of which he has apologised for, which May has branded "unacceptable".
"Whenever there is something that I find unacceptable, I will say that to Donald Trump," May, Britain's second female prime minister after Margaret Thatcher, told the BBC.
May flies to the United States on Thursday, meeting Republican leaders in Philadelphia before heading to Washington for talks at the White House on Friday.
She will then fly straight to Turkey for talks with President Recep Tayyip Erdogan on Saturday, where she will also discuss possible post-Brexit trade ties.
Turkey has been part of a customs union with the EU for some goods since 1996 and May has said she wants to strike a tailor-made customs deal with Brussels.
On her trip to Washington, May has said she will highlight her support for free trade, but also the concerns of those who feel they have lost out -- a factor in the votes for Brexit and for Trump.
May told the BBC this week that she was hoping for "early" talks on a US-UK trade deal -- although the European Commission pointed out that Britain cannot start formal trade negotiations until it leaves the bloc.
Experts have also warned that any deal is far from imminent as agreements take years to negotiate.
The premier has promised to launch the two-year divorce proceedings in March, but has already had tentative trade talks with India, Australia and New Zealand.
There are numerous obstacles to overcome, however, not least whether the US automotive industry will agree to lower tariffs on incoming British cars, and different standards on agriculture.
The president's reference to the US-led NATO military alliance as "obsolete" has also caused alarm across the Atlantic.
Britain's close ties with the United States are a cornerstone of its foreign policy, along with the commitment to NATO.
May spoke on Sunday to NATO chief Jens Stoltenberg and promised to reiterate to Trump the alliance's role as the bulwark of Western defence.
"From the conversations the prime minister has had with President Trump already, he has signalled his commitment to NATO," May's spokeswoman added.
Syria, terrorism and Russia will also feature in the talks, as will the 2015 Iranian nuclear deal, which Britain helped agree and which Trump has denounced.
Britain has long viewed itself as a bridge between the United States and the EU, a vital strategic position that some fear is threatened by Brexit.
Trump's criticism of the EU -- he warned other countries may follow Britain out the door, and attacked Germany's decision to let in refugees -- also puts May in an awkward position.
"She doesn't want to alienate the Europeans when she's got this huge negotiation coming up," said Quentin Peel, an associate fellow in the Europe programme at the Chatham House think tank.
"At the same time she does want to say to her domestic audience that actually ditching the Europeans is not a complete disaster because I've got the Americans."