Juncker said the same.
"Half memberships and cherry-picking aren't possible," he told Bild. "In Europe you eat what's on the table or you don't sit at the table."
The opposition is out in full force however, and Labour's Keir Starmer said the opposition would continue to hold the government to account, claiming May had been vague about her plans and had failed to prepare for the "clear dangers" of not reaching a deal at all.
Stephen Gethins, the Scottish National Party's Europe spokesperson at Westminster, said the announcement "shatters beyond repair any notion or position that the Prime Minister is seeking a UK-wide agreement."
"For nine months since the EU referendum," he continued, "there has been no attempt by the UK government to seek a meaningful discussion or agreement with the devolved administrations."
Scotland's First Minister Nicola Sturgeon, who has demanded a second referendum on Scottish independence, says Scotland risks leaving the EU against its will, and accused May of failing to engage with her on talks about Scotland's future.
May vehemently disagreed with Sturgeon's demand that the referendum be held between late 2018 and early 2019, saying it "wasn't the right time" for a vote.