It's unlikely the bill will reach Obama because Senate Democrats also oppose the bill.
Obama called the measure a distraction from ongoing negotiations on a full-year spending bill.
Budget negotiators in Washington have been working around the clock to try and agree on a budget ahead of Friday's deadline. If both sides can't agree on a budget, the government will shut down at midnight.
President Barack Obama and congressional leaders met late into the night at the White House, and some progress was apparently made. The president said outstanding issues were narrowed and clarified.
"I remain confident that if we're serious about getting something done, we should be able to complete a deal and get it passed and avert a shutdown. But it's going to require a sufficient sense of urgency from all parties involved," Obama said.
House Speaker John Boehner called the meeting a "productive conversation." But there is still no deal.
With the Republicans in control of the House, the question is not whether to cut from the federal budget, but how much to cut. Republicans want about $60 billion in cuts, but Democrats said they'll agree to about $33 billion in cuts.
In an interview with "Good Morning America" Thursday morning, Boehner responded to allegations he won't reach an agreement with Democrats because of tea party pressure.
"I'm going to fight for the best deal I can for my team," said Boehner. "Listen, there's no daylight between the tea party and me. They want us to deal with this crushing debt that's going to crush the future for our kids and grandkids. There's no daylight there."
Even if the leadership agrees to a framework, both the House and the Senate need to pass a bill the president can sign by Friday night or the federal government runs out of money.
Some possible effects of a government shutdown:
- 800,000 federal workers would be furloughed.
- You still have to file your tax return by April 15, but any rebate checks will likely be delayed.
- The federal government would stop guaranteeing home loans in this already shaky housing market.
- National parks, such as Yosemite, would stop allowing visitors in.
- Checks to members of the military could be delayed. They would receive back pay, but only after a deal is reached.
What won't be affected:
- Social Security checks and Medicare payments would still be paid.
- There would be no change in U.S. military operations around the world or U.S. aid to countries such as Japan.
- Air traffic controllers keep working.