"Could you stop funding in the House? Maybe. Could you stop funding in the Senate? Don't think so, but maybe. Could you override a veto of that? I don't think so."
Donohue's comments come as conservative groups seek to use the looming expiration of government funding to deal a major blow to ObamaCare.
Their strategy, which could cause a government shutdown, has gained some GOP support in the House and Senate but faces strong opposition from establishment Republicans.
The GOP leadership has not signed on, and House Majority Leader Eric Cantor (R-Va.) recently suggested that the push would not be viable unless it gains some Democratic support.
The other side, bolstered by Tea Party-affiliated groups and pundits, argues that September is the last chance to thwart the healthcare law before its insurance exchanges open for enrollment.
The battle will come to a head in late September as lawmakers seek a deal to fund the government starting Oct. 1.
In his interview, Donohue noted that the Chamber was an early opponent of the Affordable Care Act but said the law "is now there."
"Why don't we face up to the fundamental reality that there are things that need to be done in healthcare, and that we need to get together and make some of those things happen," Donohue said.
He spoke on C-SPAN's "Newsmakers" program.