European Union leaders, tired by the serpentine Brexit crisis, must decide on Wednesday whether to grant May, who has asked for a postponement until June 30, a further delay.
Britain's pro-Brexit Conservatives are protesting angrily against Prime Minister Theresa May's decision to seek the opposition party's help in finding a compromise Brexit agreement.
Three days of cross-party talks so far have ended with no agreement.
Rees-Mogg warned that the decision to meet with the hard-left opposition leader "risks giving a degree of credibility" to Jeremy Corbyn and of "undermining the general thrust of the Conservative argument that he is a Marxist who would be risky to this nation's interests".
Theresa May will head to Berlin and Paris for last-minute talks with German Chancellor Angela Merkel and French President Emmanuel Macron.
In a bid to end the deadlock with Labour, the Prime Minister is considering offering MPs a vote on whether to hold a referendum on any deal agreed between on Brexit, according to the Daily Telegraph.
May will meet the two leaders on Tuesday, their offices announced on Monday, the day before the summit where she is expected to ask the bloc for another delay to Brexit.
She said: "It'll mean compromise on both sides but I believe that delivering Brexit is the most important thing for us".
Labour wants a customs union with Brussels, something May consistently ruled out as it would prevent Britain striking trade deals with the rest of the world. If none is granted, the United Kingdom could be subjected to a no-deal Brexit as early as Friday.
In a video message recorded in her Chequers country retreat, Mrs May said both sides will have to compromise in the cross-party talks with Labour.
May heads to Berlin and Paris on Tuesday to meet Chancellor Angela Merkel and President Emmanuel Macron and will be phoning other leaders before setting out the case for another delay at Wednesday's European Union summit in Brussels.
This is when the United Kingdom is scheduled to leave the European Union after MPs repeatedly rejected the Prime Minister's deal.
The Labour MP resisted calling for it to take place until it is all finished, but questioned whether or not Britain's consistution is still fit for goal because it did not appear to be holding the prime minister to account.
The UK has already blown its first Brexit date, March 29.
The Cabinet Office said the elections would automatically be cancelled if the United Kingdom left before then.
Shadow business minister Rebecca Long-Bailey, a member of Labour's negotiating team, said while it was "disappointing" that there had not been any shift in the Government's red lines last week, "the overall mood is quite a positive and hopeful one".
The bill, which has received its final rubber stamp approval from Queen Elizabeth, gives MPs the chance to make legally binding changes to May's requested departure date during a debate scheduled for Tuesday.