Dozens of Tory MPs have called for Mr Cummings to quit his post, but senior ministers and the Prime Minister have backed the controversial adviser.
Mr Johnson's approval ratings also plummeted to -1 per cent following public backing of Mr Cummings, amid a growing revolt among Conservatives.
With the controversy over Mr Cummings raging on, it is understood MPs will have a maximum of 20 minutes in a 90-minute session to probe the situation when Mr Johnson appears before the Commons Liaison Committee on Wednesday. Other aspects of the Coronavirus crisis will also be discussed in the 20-minute slot.
Senior Tory backbencher Tobias Ellwood took to Twitter to note he would be among the chairs of Commons committees on the Liaison Committee not able to ask questions.
Asked about the situation regarding Mr Cummings, Liaison Committee chairman Sir Bernard Jenkin said: "I have got no intention of preventing any subject any member of the committee wants to raise."
The comments follows controversy over Sir Bernard's appointment to the committee, with some MPs saying he is close to the Prime Minister.
Former minister Mr Ellwood, chair of the Defence Select Committee, tweeted on Tuesday that he was looking forward to questioning the PM, but posted on social media later: "So I'm not invited to attend."
He listed a number of questions he would have asked, including: "Why was no single situation centre established?"
In statement, Mr Jenkin said that the whole committee had agreed the format for the session.
And that the "evidence session with the Prime Minister should, in its entirety, cover the Government handling of the coronavirus pandemic".
Among those questioning the PM will be Labour chairwoman of the Home Affairs Committee Yvette Cooper, and Tory chairman of the Health Committee Jeremy Hunt.
Douglas Ross, the parliamentary under-secretary of state for Scotland, said on Tuesday that he could not remain in government after hearing Mr Cummings' efforts to defend his trip from London to Durham despite the coronavirus lockdown.
Dozens of Conservative MPs have said Mr Cummings should go despite ministers seeking to protect the controversial adviser.
Mr Cummings said he had driven to Durham to isolate in a property on his father's farm because of concerns over who would care for his four-year-old son if both he and his wife were incapacitated by Covid-19.