Democrats oppose the incremental approach, saying it amounts to conservatives choosing to fund programs and services they like.
And Obama would veto such measures if they reached his desk, the White House has said. On Friday, it said the president would sign a measure expected to pass Congress guaranteeing back pay for federal workers who are furloughed because of the shutdown.
The Pentagon may announce as soon as this weekend a plan to bring up to 400,000 furloughed civilian employees back to work, according to two Defense Department officials. CNN has learned the plan is in the final stages of being written and approved.
But even if that happens, another 400,000 government employees could still be furloughed. Others who are considered "essential" would work, albeit they won't get paid until the shutdown ends -- something that could take days, weeks or months more.