The White House says the House bill would advance a narrow ideological agenda and threaten the economy. It says the bill pushes the government toward a shutdown.
Obama spokesman Jay Carney also said any Republican who votes for the bill is "voting for a shutdown." He noted that House Republicans have tried and failed to delay or eliminate the law's funding more than 40 times.
Earlier in the day, Senate Majority Leader Harry Reid said his Democratic-led chamber was certain to kill legislation moving through the House to delay Obamacare for one year and repeal a medical device tax that would be attached to a government-funding bill.
(Read more: House bill delays 'Obamacare' 1 year, pays troops)
"After weeks of futile political games from Republicans, we are still at square one: Republicans must decide whether to pass the Senate's clean CR (continuing resolution to fund the government beyond Sept. 30), or force a Republican government shutdown," Reid, a Nevada Democrat, said in a statement.
The Senate is unlikely to consider any government-funding bill approved by the House until Monday, a Senate Democratic aide told Reuters.
The House is attempting to pass legislation on Saturday that Reid warned would be rejected in the Senate.
The bill cleared a procedural hurdle in the House of Representatives on Saturday evening.
By a vote of 231-191, the Republican-controlled House set up final debate of the legislation with a vote on passage expected soon.
—By The Associated Press with Reuters