BBC: President George W Bush has said that legislators will "rise to the occasion" and pass the proposed $700bn (£380bn) Wall Street rescue plan.
He said disagreements remained as "the proposal is big and the reason it's big is because it's a big problem".
Senate Majority Leader Harry Reid, a Democrat, said lawmakers would stay in session until a deal was reached.
But rebel Republicans remain unhappy at the plan to buy mortgage-backed assets from US banks.
However there were some positive signs later on Friday, when Democratic House of Representatives Speaker Nancy Pelosi said progress was being made on a financial rescue bill.
She said Congress was "back on track" in its efforts, and that lawmakers would continue to work over the weekend to reach agreement.
And Barney Frank, Massachusetts Democrat Representative and chairman of the House Financial Committee, said: "I am convinced that by Sunday we will have an agreement that people will understand on this, on this Bill". Bush Says Bail-out Will Be Passed >>> | September 26, 2008
Watch BBC video 1: President Bush on the ongoing bail-out talks >>>
Watch BBC video 2: Senators Harry Reid and Chris Dodd lay out their terms >>>
The Dawning of a New Dark Age – Paperback (US) Barnes & Noble >>>
The Dawning of a New Dark Age – Hardcover (US) Barnes & Noble >>>
