The Government had said the Withdrawal Agreement Bill (WAB) would be published tomorrow, and a vote at second reading would take place in the week beginning June 3.
However, the legislation was not announced when the forthcoming Commons agenda was published on Thursday, and on the likeliest date for a vote - Friday 7 June - parliament is not currently scheduled to be sitting.
Mr Spencer indicated that the government did still intend to push for a vote at second reading in the first week of June.
Briefing journalists, Mrs May’s official spokesman said that agreement on the parliamentary schedule in that week had not yet been reached through the “usual channels” - meaning between party whips.
The Downing Street spokesman added that the Prime Minister “will have further discussions with ministers later today” about the WAB, signalling that she intends to continue despite the immense pressure for her to quit.
She faces a showdown meeting on Friday with Sir Graham Brady, the chairman of the powerful 1922 Committee of Conservative MPs, where she is expected to be told to quit by 10 June or face further attempts to force her out.
1922 Committee treasurer Sir Geoffrey Clifton-Brown told the Press Association on Thursday: "I want her to give a timetable for when she will go.
"I think this blank denial from Number 10 today may be a smokescreen because she does not want to influence the outcome of the European elections.
"Maybe she will still quit tomorrow."
Asked what would happen if the PM did not announce a resignation date, Sir Geoffrey said: "I think there will be overwhelming pressure for the 22 to change the rules and hold a ballot on confidence in the Prime Minister."
Foreign Secretary Jeremy Hunt, who followed Scottish Secretary David Mundell in asking for a meeting with Mrs May on Thursday, insisted she would still be PM when US President Donald Trump makes a state visit to the UK from June 3.
Mr Mundell is not expected to meet the Prime Minister as he has returned to his Borders constituency to vote in European elections.
Sir David Evennett is the latest Conservative to demand Mrs May's resignation.
Previously viewed as a loyalist, the Bexleyheath and Crayford MP used European Parliament election day to insist Mrs May must go.
He tweeted: "Theresa May must now resign. We need a new PM a new Cabinet and a new approach to Brexit."
Reports suggest the 1922 committee's executive took a secret ballot on bringing a confidence vote forward, and could release the results if Mrs May fails to set a firm exit date on Friday.
In a further sign that Mrs May intends to stay on in Downing Street, the Government announced that Ms Leadsom was being replaced as Commons Leader by junior Treasury minister Mel Stride.