After Mrs May addressed the 1922 Committee of backbench Tory MPs on Monday, some of those present suggested the PM would consult more with business on her approach to the talks.
Mrs May's authority has been severely diminished after a disastrous general election which saw her lose her Commons majority and a deal with the DUP looks vital for the continuation of Tory rule.
Anna Soubry, a Conservative member of Parliament, said she could not predict when May might go, but called the prime minister's position "untenable".
Downing Street has insisted that Thursday's general election - which Theresa May had hoped would strengthen her mandate for negotiations but ended up creating a hung Parliament - will not change the approach to Brexit it set out previous year.
May had planned a clean break from the EU, involving withdrawal from Europe's single market and customs union and limits on immigration from the EU.
Britain's Brexit minister, David Davis, has backed May, saying claims made by former finance minister George Osborne that she is a "dead woman walking" are wrong and self-indulgent.
But May faces a hard balancing act: Divisions over Europe helped sink the premierships of Margaret Thatcher, John Major and David Cameron, and many of her lawmakers and party membership support a sharp break with the EU.
The Conservatives are now trying to secure the support of Northern Ireland's 10 Democratic Unionist Party lawmakers to assure passage of May's program. The DUP are known to hold views which many in the rest of the United Kingdom do not support (they are anti-abortion, against same sex marriages and unsympathetic to the gay and trans-gender community, for a start), but critically, their colleagues are stakeholders in the devolved government for Northern Ireland which was set up as a result of the Good Friday agreement as part of the solution to "the troubles" in the province.
British Prime Minister Theresa May attempts to form an alliance to cling on to power before heading to Paris Tuesday, leaving the EU's dismayed Brexit negotiator Michel Barnier wondering when exit talks will begin.
What we can take away from this situation for now is that Britain could be headed for another general election.
May has said that the party, with its 10 crucial MPs to make up a majority in the House of Commons for the Conservatives, will have no veto on key policies.
The prime minister's most prominent potential rival, Foreign Secretary Boris Johnson, sought to quash any suggestion that she would be ousted imminently.
A minority party has an agreement with another party or parties to ensure it wins votes of confidence - generally considered on the Queen's Speech and on the Budget.
In a cabinet reshuffle, and May appointed Michael Gove, with whom she has clashed in the past, as environment minister and two of May's closest aides, who many blamed for the election result, resigned in a bid to quell dissent.
"I need a British delegation on the other side of the table, a head of the British delegation that is stable, accountable and that has a mandate", Barnier said.
He told ITV that he is an "unswerving supporter" of Mrs May, and that there is a distinction between "running a campaign and running a country".