It was broadly flat at $1.3032 by 1520 GMT on Friday after jumping up and down on mixed messages about progress in UK-EU talks.
He replied: "I will always do what I believe is in the best interests of the country".
May, once a reluctant supporter of European Union membership who won the top job in the political chaos following the 2016 referendum, has promised to give lawmakers a chance to decide what to do about Brexit on February 27 unless she can bring back a deal.
In a joint statement issued after Wednesday's meeting, the British prime minister and Mr Juncker acknowledged they were in a race against time to reach a workable deal before the scheduled date of Brexit on March 29.
Other deals the government said it was either unlikely or unable to replicate in time included those with Algeria, Andorra and Turkey. Some EU members have assessed that an agreement is "imminent", but the lack of any mention about a common ground that could be put on paper has not come to fruition, despite several optimistic rumblings from the media that a declaration could be expected.
The bloc says it is essential to avoid customs controls on the new EU-UK border with Britain's troubled province of Northern Ireland.
"But that will depend on the progress that's made over the next few days".
"We are determined to get a deal".
If May and Juncker can agree upon a strategy on Wednesday, EU and United Kingdom officials would then be able to produce documents to give force to the new plan.
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The Italian clung to the positives. "I was only anxious about my position when I was in League 2 in Italy, not now". Aside from United-Wolves, the other all-Premier League tie will be Watford hosting Crystal Palace .
Alternative arrangements could replace the backstop - but only in the future.
On Sunday, Mrs May will be attending a two-day EU-League of Arab States summit in the Egyptian Red Sea resort of Sharm el-Sheikh with about 20 EU leaders, including German Chancellor Angela Merkel and Irish Prime Minister Leo Varadkar.
Labour has accused Mrs May of deliberately running down the clock in order to increase the chances of getting her deal through the Commons.
"We have agreed that work to find a solution will continue at pace".
The backstop is designed as an insurance policy, that, in the event that the two sides can not reach an agreement before the United Kingdom withdraws from the EU, Northern Ireland will remain within the European Union's regulatory and customs arrangements indefinitely to prevent the emergence of a hard border. I've been of the opinion for a while that the European Union will offer something more acceptable to the U.K.as we approach the final minutes.
"Some of my colleagues have got to recognise that the game they have thus far been playing with regards to this whole process is not going to end well for them and could potentially end with the delaying of, perhaps even no Brexit - which some of us have spent a lot of our parliamentary and political careers campaigning for", he said.
May has promised to give parliament a chance to decide what to do about Brexit on February 27 unless she can bring back a deal.
But the premier wants to be able to show Parliament that she's made significant progress on getting the Irish backstop fixed by next week, according to a person familiar with her plans.She'll attend an European Union summit in Egypt on Sunday, and talks on Brexit are expected on the sidelines.