DUP sources have taken aim at the lack of "negotiating experience" on the Conservative side, a devastating criticism, just days after the separate Brexit talks also got underway.
And there's also a bit of an uncomfortable story dominating some parts of the Northern Ireland media which Arlene Foster won't enjoy.
May, who called a snap election expecting to fatten her party's majority, is promising her minority government will be one "that consults and listens".
Instead, she lost seats and still hasn't secured a deal with another party to insure Parliament will back the government's agenda.
Asked if an agreement was close, Mr Green replied: "There is still the possibility - there's every possibility - of a DUP deal".
"The talks have been taking place in a constructive way", the First Secretary of State told BBC Radio 4's Today programme.
However, religious violence might have ended as a result of the conclusion of the GFA, but political differences and divisions have continued to dominate the Northern Ireland Assembly over the years. "The talks are going on, they are going well".
As Gerry Adams, leader of Sinn Fein, has warned, the marriage between the Tory Party and the DUP may threaten peace in Northern Ireland, it got me thinking: Does Theresa May really have no better choice for partnership other than the DUP?
"If we have learned nothing else in the last ten years we have surely learned that the future of the United Kingdom as a constitutional union is not to be taken for granted".
Keith Richards, PFS chief executive, said: 'We can't ignore the demographic and economic pressures facing our economy, and the new government has to take responsibility for easing these pressures by making hard decisions and introducing courageous but prudent measures so that the public have a choice of mitigating any personal impact on them and their families.
The speech is expected to set out a raft of new laws needed to implement Brexit, plans to strengthen counter-terrorism powers and a series of bills created to reform Britain's infrastructure and economy in preparation for life after the EU.
New pension policy is not expected to feature much in the speech.
Queen Elizabeth II will outline the government's legislative program with far less pageantry than usual Wednesday in a speech expected to be dominated by a discussion of Britain's plans for leaving the European Union.
The Belfast North MP said the economic outlook of Northern Ireland would be "easier to predict" with "stable" government both in Belfast and Westminster. "The only solution I can see, when I think about it, is if you really don't want to have a border, is not to leave the single market and not to leave the customs union".