But a deadly fire at a tower block in London delayed the announcement of any deal.
Ms Foster said the talks deadline remained "realistic".
Editor's Remarks: Having been relieved of her parliamentary majority, May is now clawing back support from senior Tories that she relegated to the party's fringes almost a year ago.
They also said the rally would protest the DUP's record on "access to abortion", and that if the deal goes through the Conservatives would be joining with a party "known to promote policy which restricts the rights of women and LGBT people".
Despite the uncertainty over her ability to govern, May had confirmed that Brexit negotiations - expected to be the most complex worldwide talks Britain has held for decades - would begin as planned next week.
On a visit to Paris on Tuesday evening, where she met with French President Emmanuel Macron, May described the talks with the DUP as "productive".
"It's a unity of objective, having voted to leave the European Union, that their government gets on with that and makes a success of it".
But with so much at stake for Britain and its $2.5 trillion economy, pressure was mounting on May from within and without her party to heed other voices.
"There is very little time left". The finance ministry declined to comment.
"And if that wasn't enough, calling an unnecessary general election purely for the self interest of the Conservative Party and having mucked that campaign up they are now putting the country in hock to the DUP".
"Delay to deal with DUP means likely postponement of Queens speech; and possibly Brexit talks", BBC political reporter Norman Smith said on Twitter. Once done, however, Brexit would be hard to reverse.
Mrs May needs the votes of the DUP's 10 MPs to prop up her minority administration.
"I cannot see for the life of me how you can be a neutral facilitator in bringing the parties together, at a very risky time for Northern Ireland politics to get self-government and the legislative assembly back up and running, when your prime ministerial life and your government's life depends on one of the most influential parties - the biggest party - in Northern Ireland", Lord Hain said.
"There is an irony to being lectured by some about our role in the national government of the United Kingdom when Sinn Féin want to be in government here in the Republic of Ireland", she said.
If the talks fail it may bring back direct rule from London which after all the good work of the Good Friday Agreement and the time both Sinn Fein and the DUP shared power together would be a complete shame.
The DUP and Sinn Fein are taking part in Thursday's talks at Downing Street, along with smaller parties.
It is not yet clear whether the European Union withdrawal talks will go ahead on that day, although Brexit Secretary David Davis has said they will start "next week".