Business and investors want clarity about the terms of Brexit as soon as possible, because they need to know what kind of access United Kingdom companies will have to Europe's vast free trading area in future.
Under pressure from Conservative cabinet ministers, May accepted the resignation of her two top aides, her co-chiefs of staff Nick Timothy and Fiona Hill, on Saturday. "I'm sure many of them will want to vote for government measures needed to execute our departure from the European Union".
May's room for maneuver has been eroded by the election drubbing which saw the Conservatives lose their majority in Parliament, and she has kept many ministers in their jobs.
Many others have been less vocal, but with 12 fewer Conservative seats in parliament than before the election, you can be sure many are smarting if not seething, meaning a leadership challenge could soon be on the cards.
The exit poll pointed to an extraordinary failure for May, who was enjoying opinion poll leads of 20 points and more when she called the election.
The vote returned a small increase in women MPs from 191 in the last election in 2015 after which Britain ranked 46th in an index of parliaments based on the number of female lawmakers, behind many European countries and others such as Rwanda, Cuba and Belarus.
But her decision to call the general election seems to have backfired, according to the exit poll, leaving the country in even more uncertainty, something financial markets don't react well to.
Video: Where did it all go wrong for Theresa May?
Defence Secretary Michael Fallon said the government was not looking at a formal coalition but would seek assurances that the DUP would vote with May "on the big things" such as the budget, defence issues and Brexit.
In 2015, Northern Ireland health minister and DUP senior member Jim Wells resigned after police started an investigation into comments he made linking gay marriage to child abuse. "We want to see Brexit work, we want the Union strengthened".
"If she has an ounce of self respect, she will resign".
If the June 8 General Election ends in a hung parliament, it could be a matter of days or weeks before the final form of the next government is settled.
The move was denounced by Labour leader Jeremy Corbyn, who called on her to stand aside and allow him to form an administration, declaring: "We are ready to serve". Politicians across all the parties must come together to deliver in the national interest so the UK's GBP110bn (US$140.47bn) food and farming industry can continue to thrive.
Labour leader Jeremy Corbyn, whose energetic campaign defied predictions of a crushing defeat, told May to quit, saying she had "lost votes, lost support and lost confidence".
"So a fascinating time - Theresa May staring down the camera lens and telling the country: 'I am still in charge'".
May announced the party would try to work with Northern Ireland's Democratic Unionist Party, an alliance that is fraught with difficulties.
"If they are going to squeeze out some concession from the Tories, is that concession going to frustrate Sinn Fein to the point where the prospect of devolution disappears and there is direct rule from Westminster again in Northern Ireland".
Any Prime Minister would be unlikely to ask the Queen to present a programme if they did not believe it would secure the support of a majority of MPs in the Commons.
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