Republican leaders in both chambers don't want a shutdown now over the spending issue, for political and negotiating reasons.
They fear the optics of Republicans being blamed for a shutdown, and also want to exert as much leverage as possible for the GOP's agenda at the upcoming deadline to raise the federal debt limit.
However, Boehner needs backing from the 40 or so tea party conservatives in the House in order to have a spending plan pass with full support from his Republican caucus.
The tea party opposition to the Senate version would mean it could only pass the House with support from all Democrats and some Republicans, which would further weaken Boehner's already shaky leadership of his caucus.
Tea party conservatives want to halt Obamacare now, just as full implementation of its individual health care exchanges begins in the new fiscal year starting Tuesday.
More moderate Republicans, such as veteran Sens. John McCain of Arizona and John Cornyn of Texas, criticize the strategy of tying a government shutdown to undermining the health care reform law passed by Democrats in 2010 and upheld by the Supreme Court last year.
Debt ceiling deadline
The shutdown showdown comes a few weeks before another fiscal deadline -- the need to raise the nation's debt ceiling so the government can pay all its bills.
Treasury Secretary Jack Lew said this week the limit on how much the government can borrow must be increased by October 17 or the nation could be technically in default.
Analysts warn of severe economic impact from any doubt cast over whether the United States would fail to meet its debt obligations. A similar bout of congressional brinksmanship over the debt ceiling in 2011 led to the first-ever downgrade of the U.S. credit rating.
However, Boehner faces the same rift in his caucus over the debt ceiling issue, with tea party conservatives pushing for to undermine Obamacare and fulfill other Republican priorities in return for what Obama calls the responsibility of Congress to make sure America can pay its bills.
On Thursday, Boehner had to delay introducing a GOP debt ceiling plan after conservatives complained the proposed package failed to include enough budget cuts and significant changes to entitlement programs.
The initial proposal by House GOP leaders, which would raise the debt ceiling for a year, included a one-year delay of Obamacare, provisions to roll back regulations on businesses, tax reforms, and approval of the Keystone XL oil pipeline.
House conservatives push Boehner
However, conservatives wanted more.
Republican, Rep. Cynthia Lummis of Wyoming told CNN that she was undecided but wanted to see deeper budget cuts on the measure.
"I came here to cut spending and to reduce the size of the federal government, so when those opportunities arise I want to take advantage of them," Lummis said.
Obama said Friday that the GOP strategy amounts to threatening to "burn the house down simply because you haven't gotten 100% of your way."
"That's not how our democracy is supposed to work," he said, repeating his past insistence that he will not negotiate under threat of a U.S. default because Congress failed to increase the debt ceiling.
White House spokesman Jay Carney told reporters on Thursday a one-year delay in implementing Obamacare's individual mandate for people to obtain health insurance would undermine a key provision of the program that prohibits the denial of coverage due to pre-existing conditions.