Six months after beginning the two-year process of withdrawing Britain from the European Union, the Conservative leader has yet to set out in detail what she wants from the divorce.
The lack of clarity was reinforced when May's foreign secretary, Boris Johnson, laid out his own vision for Brexit in a newspaper article last weekend.
The prime minister has insisted her government was "driven from the front", but Johnson's intervention has raised the stakes.
Businesses are also watching closely.
The head of the CBI lobby group of business leaders, Carolyn Fairbairn, warned the risks of leaving the EU without a deal felt "all too real".
A fourth round of talks with the European Commission are due to begin next week and the question of Britain's financial settlement remains a significant stumbling block.
Without progress, EU leaders are unlikely to accept Britain's request to move the negotiations on to the future trading relationship at their next summit in October.
"Theresa May needs to make a serious offer on the money that she hasn't made so far. And on the transition, she needs to say what she wants."
The Financial Times reported that May would offer to meet Britain's commitments under the current EU budget, which runs to 2020, worth at least 20 billion euros (USD 24 billion).
This would mean continued payments during a transition deal that Britain wants to bridge the gap between Brexit in March 2019 and the implementation of a new trading arrangement.
In his 4,000-word article, Johnson -- a leading voice for Brexit in last year's referendum campaign -- argued for a clean break with the EU, including on financial matters.
The foreign secretary, who has long held leadership ambitions, subsequently denied reports he had threatened to resign, and insisted the cabinet was as united as a "nest of singing birds".
Johnson's move highlighted the fragility of May's position, after her Conservatives lost their parliamentary majority in June's snap election.
Senior ministers are expected to join the prime minister in Florence, a place her office called the "historical heart" of Europe.
A cartoon in the Daily Telegraph today had Johnson grappling with other ministers and snakes dubbed "Brexitus", an apparent reference to a sculpture in the Uffizi Gallery.
The Times, meanwhile, depicted him as King Kong, holding May in one hand as he swung on the famous dome of Florence's cathedral.
Johnson has long cultivated a reputation as a lovable buffoon, but European agriculture commissioner Phil Hogan said he was a "diminished figure" -- and warned May against following his lead.
The prime minister has called a special cabinet meeting for tomorrow morning, where she is expected to brief ministers -- and ensure they fall in line.
Former Conservative leader William Hague urged colleagues to rally round.
"The period of negotiating publicly with each other is over... The time for negotiating in earnest with the EU has begun," he said.
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