(CNN) Theresa May , Britain's embattled Prime Minister, appears to be on the verge of delaying the Queen's Speech -- a key annual event in which the government lays out its policy agenda for the coming year.

At the regular daily press briefing, Downing Street pointedly declined to confirm whether the event, which was due to take place on June 19, would go ahead as planned.

The BBC and Sky News quoted unnamed sources saying it would be delayed by a few days as May struggles to reach a deal to ensure the support of the Democratic Unionist Party (DUP), essential if she is to command a majority in the UK parliament.

Traditionally, the first Queen's speech following a general election puts forward the winning party's legislative program and a list of laws the party hopes to push through in the coming year.

But after a bruising election result that left Britain with a minority government, May cannot be sure of getting enough votes in the House of Commons to have the Queen's Speech approved. If the Queen's Speech is voted down, an opposition party could force a confidence vote, likely bringing down the government.

Brexit Secretary David Davis appeared to concede that "it's a matter of practicality" when it comes to what the party can get through. He told Sky News on Monday that it was likely parts of the party's manifesto would have to be "pruned" now that Conservative lawmakers are without a parliamentary majority.

Why delay?

The party's only chance of achieving an overall working majority is to partner with the DUP, a political outlier from Northern Ireland, which is demanding a package of measures on finance in return for support in Parliament. Details of the deal are yet to be reached.

An update on whether the Queen's Speech will go ahead is expected soon from the office of the Leader of the House of Commons, Andrea Leadson, the Downing Street spokesperson told CNN.

Should the speech at the state opening of parliament be delayed, the monarch's diary will also need to be consulted before a new day can be announced.

But, according to the UK's Press Association, it will inevitably clash with one of the Queen's favorite events -- Royal Ascot, which begins on June 20. The Queen had been slated to appear at all five days of the annual horse-racing spectacular.

'I got us into this mess, I'll get us out'

As the new week got underway, May held her first reshuffled cabinet meeting since the vote at Downing Street.

Ordinarily, after an election victory, it would have been a moment for self-congratulation. But Monday's meeting would likely have been a tenser affair, with discussions about how an arrangement with the DUP could be concluded.

Later on Monday, the Prime Minister faced Conservative backbench MPs -- known collectively as the 1922 committee.

May needed to convince her furious MPs that she has a plan going forward or potentially face a leadership challenge . Before the 1922 members for over an hour an a half -- markedly longer than normal -- at the House of Commons, the British Prime Minister apologized for the party's stinging election performance.

"I'm the person who got us into this mess, and I'm the one who will get us out of it," she told MPs, according to the Press Association.

And judging by the optimistic reaction from MPs after the meeting, it looks as if the prime minister may cling to her job for a little while longer.

"I think the prime minister, this evening in my committee, very firmly took responsibility for the decision to call the election and, indeed, for the nature of the election campaign, and was right to do so," Graham Brady, the committee's chairman and Conservative MP, told CNN.

He commended May's decision to stay on as leader in the face of a bittersweet result rather than stepping down, calling it "the right thing to do" and said there was little desire to replace her at this time.

"There's no mood in the Conservative party for yet another leadership election. We had a leadership election only a year ago," Brady said. "I think are all determined to pull together behind Theresa May and I think colleagues admire her steel and determination and dedication to serving the country."

Brady said the timing of the Queen's Speech was still being worked out, adding that the important thing was to "get it right" and ensure it is voted through the House of Commons with a majority.

He added: "One can understand that might take a little longer than if it were a single party with an overall majority."

PM continues to focus on Brexit talks

Formal negotiations for Britain's departure from the European Union had been expected to begin on June 19, the same day as the Queen's Speech. Now this timetable is also in doubt.

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Before the election, May had taken a hard position on Brexit, pushing forward with plans to remove the country from the EU's single market in a bid to regain control of Britain's borders and immigration.

With her snap election gamble backfiring, many now believe the election result could dramatically change the final outcome of Brexit negotiations and push her towards a more conciliatory, softer departure.

On Monday, the prime minister's spokesperson reiterated that securing "the best possible deal for the whole of the United Kingdom" remains one of May's primary objectives.

He said the prime minister will continue to act as chief negotiator for the upcoming talks and Brexit secretary David Davis will be involved in the "detailed aspects of negotiations," which were expected to start next week "but not necessarily the 19th of June."