McDonnell made the remarks to Reuters in London Wednesday, saying that most in parliament are opposed to leaving the EU without a deal.
"We just can't go on like this," McDonnell said. "We just cannot go on with this instability, uncertainty that there is in government, day by day and sometimes hour by hour."
May’s current draft Brexit deal struck last week has faced sharp backlash, with several ministers resigning, including her Brexit minister.
The deal with the EU is not likely to be approved by the British parliament as both pro- and anti-EU lawmakers have expressed their frustration at the draft.
The overwhelming opposition has prompted some Tories as well as opposition parties to call for a vote of no confidence in May.
May, however, has not given in, warning that toppling her could further delay Britain's exit from the bloc or leaving without a deal, which would ultimately thrust the country into the unknown.
McDonnell also said that "an overwhelming majority oppose anything that smacks of being no deal."
"Then we could be into a situation of a war of attrition within parliament of amendments to legislation taking place and uncertainty continuing," he added.
May has indicated that she could gain concessions from the EU on a political declaration that would define the bases of the future relations between the two sides.
However, her opponents want changes to the 585-page deal that is mostly concerned with Britain’s departure from the EU on March 29, 2019 which includes controversial measures about how the two sides will cooperate during a two-year transition period.