He rejected the House's proposal to meet, saying "we will not go to conference with a gun to our head."
For the second time Monday, the Senate rejected a House Republican effort to derail Obamacare tied to a proposal that would avert the shutdown.
The Senate voted to table amendments that would have delayed the individual mandate in the health care law and eliminated health insurance premium subsidies for members of Congress, their staffs and the president.
In the latest volley of legislative ping pong over a short-term spending plan needed to avoid the shutdown, House Republicans were expected to meet to discuss their next steps.
"The government is going to shut down ... I don't know for how long," GOP Rep. Devin Nunes of California told CNN while leaving Speaker John Boehner's office.
Democratic Rep. Chris Van Hollen said the reason there isn't a budget is because Republicans refused to negotiate months ago.
"They want to go to conference with 45 minutes left," Van Hollen said late Monday night. "That is a recipe for a government shutdown,"
Earlier, Senate Democrats had rejected a House proposal by a 54-46 vote on strict party lines.
President Barack Obama made a previously unscheduled statement to reporters on Monday afternoon, blasting the attempts by House Republicans to undermine Obamacare that he said threaten to harm the economy with a shutdown.
"You don't get to extract a ransom for doing your job, for doing what you're supposed to be doing anyway, where just because there's a law there that you don't like," the president said.
Obama later called Boehner and other party leaders in the House and Senate, the White House said, but a Boehner spokesman indicated there was no breakthrough.
Moderate GOP revolt against Boehner?
GOP sources told CNN that moderate House Republicans were trying to galvanize what would amount to a rebellion against Boehner and their tea party colleagues by defeating the latest proposed spending plan with attached anti-Obamacare provisions.
However, a procedural vote on the measure passed with only six Republicans voting "no."
Without congressional approval of new spending legislation, parts of the federal government will begin shutting down when the current fiscal year ends at midnight, forcing agencies to furlough thousands of workers and curtail some services until there is a resolution.
"I feel sad about it. We expect more from our Congress," said Vick Temple, a worker for the Federal Aviation Administration who told CNN he faced being furloughed in a shutdown.
Polls show public opposition to a shutdown, and stocks ended lower Monday on Wall Street due to concerns over the economic impact.
Meanwhile, the two parties persisted in blaming the other side as the shutdown deadline neared.
Republican Rep. Renee Ellmers of North Carolina said on CNN's "New Day" that her party continues to be deeply concerned about Tuesday's scheduled opening of Obamacare health insurance exchanges and "keeping the checkbook out of Barack Obama's hands and the damage can be done there."
Rep. Debbie Wasserman Shultz, D-Florida, appearing alongside Ellmers, characterized the Republican strategy of tying overall government operations to at least a delay in health care changes as "irrational."
"It jeopardizes the economy and it makes no sense," she said.
On Monday morning, Obama told reporters he wasn't resigned to a shutdown, but he signaled its likelihood even as he indicated possible talks with congressional leaders.
"I suspect that I will be speaking to the leaders today, tomorrow and the next day," Obama said at a joint appearance with visiting Israeli Prime Minister Benjamin Netanyahu, who acknowledged the Washington brouhaha by thanking the president for meeting with him "on what I know is a very busy day for you."
Legislative ping pong
Last week, the Senate voted down a House GOP plan to eliminate funding for Obamacare in a short-term spending plan to keep the government running in the new fiscal year that begins Tuesday.
Democrats have pressured Boehner to give up a losing fight over Obamacare forced by tea party conservatives and instead hold a vote on a "clean" spending plan that includes no provisions seeking to undermine the health care reforms.
On CNN, Wasserman Schultz predicted that such a measure would pass easily with support from all Democrats and more moderate Republicans.
Some Republicans expressed frustration Monday with the tactics of their congressional colleagues. Veteran GOP Sen. John McCain of Arizona noted that any attempt to repeal Obamacare would fail because of Obama's veto, which would require a two-thirds majority in the Senate to overcome.
"There's not 67 votes in the United States Senate, therefore, ergo, we're not going to repeal Obamacare," McCain said. "OK? That's it. We may do this for a day. We may do it for a week. We may do it for a month. It's going to end up the same way. "
GOP Rep. Charlie Dent of Pennsylvania told CNN Chief Congressional Correspondent Dana Bash that whichever party was to blame, a shutdown will make everyone look bad.
"At this point, the hourglass is nearly empty," Dent said. "Now that we've sent over two volleys to the U.S. Senate and they rejected both."
Trying again would only yield the same result, he continued, adding that "sooner or later, we have to pass a clean resolution to fund the government before the end of the day."
"I believe the votes are there to do it," Dent said.
Obamacare a GOP focus
Obama and Democrats reject what they call Republican efforts to use the threat of a government shutdown to force negotiations on the president's signature health care reforms.
Noting that the 2010 Affordable Care Act has been upheld by the Supreme Court, they say it is settled law that voters endorsed last year by re-electing Obama over GOP candidate Mitt Romney, who campaigned on repealing it.
A new CNN/ORC poll shows that Americans are not happy about the prospect of a shutdown, which is happening because Congress has been unable to pass a budget for the new fiscal year that begins Tuesday.
According to the poll, 68% of Americans think shutting down the government for even a few days is a bad idea, while 27% think it's a good idea.
And it appears most Americans would blame congressional Republicans for a shutdown: Sixty-nine percent said they agreed with the statement that the party's elected officials were acting like "spoiled children."
Democrats, however, weren't far behind: Fifty-eight percent of respondents said they too were acting like spoiled kids.
A poll later showed public support for Congress at record low levels.
Stock traders also seemed solidly against a shutdown. The Dow Jones Industrial Average fell by more than 120 points, or nearly 1 percent, and the other two major indexes also closed lower.
Among major economic issues that could result from a shutdown: delays in processing FHA housing loan applications -- a potential drag on the housing recovery -- and the potential loss of government spending that's helping prop up the economy, said Christine Romans, host of CNN's "Your Money."
"You've got an economy right now that's very tied to government spending and government contracts, so that could have a ripple effect all across Main Street," she said on CNN's "New Day."
If the government does shut down, it would be the first time it has happened in more than 17 years. That previous shutdown, sparked by a budget battle between Democratic President Bill Clinton and a Republican Congress, lasted for 21 days.
While the military will remain on duty, as will many essential public safety, health and welfare operations, many government offices will close. About a quarter of the federal government's 3.3 million employees -- those frequently referred to as "nonessential" -- will be told to stay home from work until the shutdown is over.
Late Monday, Obama signed a bill to guarantee pay for active duty military if the government shuts down.
Attorney General Eric Holder and Defense Secretary Chuck Hagel said essential crime prevention and military services would continue, but some workers would be furloughed. Holder said he would cut his pay by the same amount as the most severely affected Justice Department employees because "we are all in this together."