Speaking alongside Slovak Prime Minister Peter Pellegrini at the European Parliament, Jean-Claude Juncker told MEPs: "I'll let you into a secret. I didn't sleep much last night because of Mrs May, but long enough to be able to dream of Slovakia."
Mr Juncker added: "We reached an agreement last night with the British Government on the terms of Brexit, and I said yesterday evening - or anyway during the night - that it was a second chance, but there wouldn't be a third chance.
"I would therefore like British MPs to support the measures, which are both British and European and which have taken form in agreed texts, an agreement at EU level."
European Commission vice-president Jyrki Katainen said if the deal was rejected the prospect of a “hard Brexit” moved closer and his advice was “fasten your seatbelt”.
He told reporters in Strasbourg: “Depending on the vote in the Commons, we are either moving forward to orderly withdrawal or hard Brexit is closer again, more close than ever it has been.
“So, keep your hands on the wheel, look forward and fasten your seatbelt.”
Earlier: Dutch Prime Minister claims 'there is no alternative' to last night's Brexit deal
Dutch Prime Minister has said "there is no alternative" to the deal agreed in last-ditch talks in Strasbourg last night ahead of a crunch vote in the UK Parliament tonight.
British Prime Minister Theresa May insists she has secured “legally binding” changes to the Brexit deal which ensure the Irish backstop cannot be permanent.
Mrs May said she “passionately believed” her Brexit deal addressed concerns raised by MPs who feared the backstop would keep the UK in a customs arrangement with the EU indefinitely.
Mark Rutte said he hoped MPs at Westminster would back the deal, adding: "An orderly Brexit is crucial for both the EU and the UK.
"I hope that the House of Commons will support the agreement reached by Theresa May. There is no alternative."
President of the European Parliament Antonio Tajani said he hopes "common sense will prevail".
"We have done everything possible to reassure the United Kingdom. We look forward to a positive vote in the Commons," he tweeted.
Mr Tajani met with Mrs May in Strasbourg last night.