With her tally of Conservative MPs slashed to 317 in last week's poll, Mrs May needs the backing of the DUP's 10 members to reach the 320 required for a working majority in the Commons.
Negotiations over Britain's exit from the European Union will begin on Monday.
Labour leader Jeremy Corbyn countered with a bit of previously unseen swagger, wearing a huge red rose - his party's symbol - in his lapel as he sparred with May and taunted her about the uncertainty surrounding the upcoming vote on her legislative program, known as the Queen's Speech.
The Northern Irish party's stance on equality has been under scrutiny this week, as numerous MPs that Theresa May will be relying on harbour actively homophobic views.
'Although I don't expect it suddenly to collapse, because there's a broad consensus that wishes it to continue, I think we have to take care with it and take care that everything we do does not exaggerate the underlying differences that still are there in the Northern Ireland community'.
The head of the Democratic Unionist Party has arrived for crucial talks on whether to support Prime Minister Theresa May's Conservatives in an alliance.
"It will take us several months to draw out the conditions of an orderly withdrawal... so let's not waste time", he said.
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The DUP is understood to be close to agreeing to its ten MPs supporting Mrs May's minority government on a "confidence and supply basis". Demonstrators denounced what they called the homophobic and sexist values of the party, and argued that a Tory pact with the DUP could put the Northern Irish peace process at risk. I am wary about it.
The EU's chief Brexit negotiator, Michael Barnier and the UK's Brexit minister, David Davis, will meet in Brussels on Monday (19 June), kicking off negotiations likely to take nearly two years. "I am dubious about it", Major said.
Northern Ireland's frontier with the Republic of Ireland will be the UK's only land border with the European Union after Brexit.
The British Prime Minister should consult with the opposition Labour Party and others on her Brexit strategy, David Cameron, May's predecessor, says, according to the Financial Times.
Ms 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 politicians and party membership support a sharp break with the EU.
Talks for a new relationship between London and Brussels will start on June 19.