However, the bill, intended to finance the wars in Afghanistan and Iraq until the end of September, would include some benchmarks to force Bush to report on the Iraqi government's progress on security and political issues, sources said.
Signs that Democrats were ready to agree to drop withdrawal timelines appeared to reflect a realisation that Bush, as commander in chief, has control over foreign wars and foreign policy.
They were also gearing up for future fights, and not seen as keen to be portrayed as unsupportive of troops locked in combat.
"We have moved the ball forward," said one source, a Democratic staffer, on condition of anonymity.
"Whatever bill the president is going to sign is going to contain some kind of benchmarks."
Final drafting of the measure was yet to be completed, or presented to Democratic members of congress, many of whom are fiercely anti-war, the sources said.
But John Edwards, former US senator running a populist campaign for the 2008 Democratic presidential nomination, immediately hit out at signs that Democrats were stepping away from withdrawal timetables.
"We need to stand our ground against this president," Edwards said in a statement.
"Congress should send him the same bill back to him again and again until he realises he has no choice but to start bringing our troops home."