Boehner said Congress had passed and Obama signed legislation last week permitting the payments, adding it was "disgraceful" for the administration to interpret the measure otherwise. He said the House would clarify the issue with a new bill on Wednesday.
In Congress, a plan by Senate Democrats to raise the debt limit by $1 trillion to stave off a possible default drew little evidence of support from Republicans.
And a proposal by Republicans to create a working group of 20 lawmakers to tackle deficit issues, approved 224-197 by the House, drew a veto threat from the White House, the latest in a string of them as the administration insists the GOP reopen the government and avert default before any negotiations on deficit reduction or the three-year-old health care law can take place.
On a day in which both Obama and Boehner appeared on live television, both men appeared to be giving ground yet yielding little if anything of substance.
At midmorning, Boehner and other Republicans seemed to soften their demands.
"I suspect we can work out a mechanism to raise the debt ceiling while a negotiation is underway," said Rep. Tom Cole, an Oklahoma Republican who is close to Boehner.
The speaker, who had previously insisted on specific changes in the health care law as the price for preventing the shutdown, told reporters, "I want to have a conversation (with Obama and Democrats.) I'm not drawing any lines in the sand. It's time for us to just sit down and resolve our differences."
Asked if he was willing to raise the debt ceiling and fund the government for a short period, the Ohio Republican sidestepped. "I'm not going to get into a whole lot of speculation," he said.
A few hours later, Obama told a news conference he was willing to negotiate with Republicans on budget and other issues if Congress passed even short-term legislation to end the crisis.
"I'll even spring for dinner again," he said, referring to his courtship of Republican senators last winter, and attempting to inject humor into a political impasse where invective has been the norm.
Ninety minutes later, Boehner was unsmiling.
"What the president said today was if there's unconditional surrender by Republicans, he'll sit down and talk," he said. Renewing his call for "a conversation" about key issues facing the country, the Ohio Republican said, "Not next week. Not next month. The conversation ought to start today."
Boehner added, "The long and short of it is, there is going to be a negotiation here. We can't raise the debt ceiling without doing something about what's driving us to borrow more money and to live beyond our means."
Privately, officials said deeply suspicious Republicans were attempting to gauge Obama's comments to see whether they might represent a concession.
Treasury Secretary Jacob Lew has said the deadline for Congress to act is Oct., 17, setting that as the day the government will exhaust its ability to borrow funds and will have to rely day-to-day on tax and other receipts to pay its bills.