"Support for Michel Barnier [EU negotiator] to continue the negotiations is strong, support for Ireland and the Irish backstop is still very strong", she claimed - although some countries such as Poland and Hungary have suggested they are concerned Brussels is pushing for too many concessions and could damage EU member-states if it fails to offer Britain a comprehensive free trade agreement.
"The PM set out her position on Monday, Donald Tusk has set out his views and the PM looks forward to face to face discussion", was Number 10's response to the request from the EU Council President for "concrete proposals" and "new facts" following the unravelling of a technical deal on Sunday over the issue of the Irish backstop.
The Prime Minister is considering the proposal to act as a "bridge" between the end of a implementation period where the United Kingdom abides by the EU's rules and regulations and singing a free trade deal.
"Theresa May must now act in the national interest, not her party interest, and break the deadlock by delivering a deal that protects jobs and living standards".
The Prime Minister brought up the possibility of an extension during meetings with European Union leaders in Brussels on Wednesday in an effort to get passed a deadlock in negotiations.
But the bloc ruled not enough progress has been made and so shelved plans for a special summit to be held next month to sign off on a deal.
"There is a message of goodwill, readiness to reach an agreement".
So uncertain was that prospect that a special European Union summit on Brexit that had been penciled in for next month to finalize a deal was taken off the table. "By working intensively and closely we can achieve that deal", she told reporters.
The EU says a time limit would defeat the point of the backstop.
Britain's Prime Minister Theresa May peers into a hot water urn during a meeting at a social group in Vauxhall from a charity working to combat loneliness at the launch of the first loneliness strategy, in Vauxhall, London, Monday, Oct. 15, 2018.
Another big date arrives on January 21, when May faces a final deadline to send a Brexit deal to Parliament.
The letter signed by former British Foreign Secretary Boris Johnson, ex-Brexit Secretary David Davis and other pro-Brexit Conservatives warned May not to "engage in a show of resistance and a choreographed argument followed by surrender" to the EU.
May and her European Union counterparts are running down the clock towards a no-deal Brexit, said Tory MP Nick Boles, who served as skills minister between 2014 and 2016.
And the Financial Times says one of the US's top market regulators has threatened to stop European banks from using American futures markets if the EU refuses to water down post-Brexit plans to oversee clearing houses. "For now, we have a no-deal", the diplomat said, adding leaders were waiting for Britain's budget, due to be presented to parliament in late October, to be passed.
The EU is willing to insert a text in to the Withdrawal Agreement a text guaranteeing it will create a UK-wide customs backstop plan in the future.
"May is testing the water by saying that she is open to an extension, but her proposal for one only as a fallback option and only for a few months, reflects her concerns about the political backlash", she said.
"They want it to be temporary, to be replaced by something better".
Repeatedly she failed to answer the hard questions on Brexit, on Chequers and on any divorce bill the United Kingdom might have to pay.