Mr Corbyn said the Government had failed to make a "big offer" in the talks aimed at ending the Brexit deadlock.
It means that Mrs May has now set five separate dates for Britain to leave the EU.
The prime minister has promised to quit as Tory leader when the first phase of Brexit negotiations, dealing with divorce terms, is complete.
Lawmaker Mary Creagh said "if Labour stands in the middle of the road on Brexit we'll get run over from both directions".
Exasperation with Mrs May boiled over after Mr Lidington, her de facto deputy, confirmed that Britain would fight the European elections in 15 days' time despite months of assurances to the contrary.
"But she hopes Parliament will agree a Brexit plan before MEPs start their session in July", May's spokesperson added.
Anger at her leadership has flared up following last week's dismal local election results, and the chairman of the 1922 committee of Conservative MPs, Graham Brady, met May on Tuesday to relay their concerns.
"Sincere cross-party collaboration must happen today to end this crisis", she said.
Meanwhile, talks on a compromise deal were continuing in Whitehall on Wednesday evening, with Labour insisting the government still needed to shift on its red lines.
Cabinet Office Minister and May's de facto deputy David Lidington said the European Union parliament vote on May 23 will go ahead, even though the MEPs elected will not take their places in Brussels if a Brexit deal is agreed.
Prime Minister Theresa May on Wednesday resisted demands from within her party to give a clear timetable for stepping down, with her spokesman insisting she would stay until Britain's exit from the European Union is finalised.
"I actually think that when we look at the Liverpool win over Barcelona last night, what it shows is that when everyone says it's all over, that your European opposition have got you beat, the clock is ticking down, it's time to concede defeat, actually we can still secure success if everyone comes together", May stated.
The Brexit Party led by former U.K. Independence Party leader Nigel Farage is drawing hundreds of people to rallies across the country with its simple narrative: Brexit has been betrayed by a London political elite.