Boehner has the power to block the bill, even though its backers say it has 225 House co-sponsors, including 61 Republicans, enough to ensure its passage if it came to a vote.
Lloyd Wood, a spokesman for the Fair Currency Coalition, said supporters would keep pressing at "the grass roots level" to demand action on the bill.
"If you can persuade enough rank-and-file Republicans, they're going to ask leadership for a vote and at the end of the day we think that's what's going to happen," Wood said.
Senator Rob Portman, an Ohio Republican and former U.S. trade negotiator, told Reuters he supported the legislation, even though he preferred the Obama administration lead a multilateral effort to pressure China to revalue the yuan.
"This is an opportunity to raise the visibility of the issue and to encourage the administration to address it more vigorously."
China has mounted an intense lobbying effort in Washington to kill the legislation.
A 12-member "Congressional Liaison Team" inside the Chinese embassy has been meeting with aides to key lawmakers, making phone calls to congressional offices and speaking to the White House on the issue, according to Chinese and U.S. officials.
The U.S. Treasury Department faces a statutory deadline on Sunday to release a semi-annual report on whether any country is manipulating its currency for an unfair trade advantage.
In five previous reports, the Obama administration has stopped short of formally labeling China a manipulator, which would require it to pursue stepped-up negotiations aimed at getting Beijing to revalue the yuan.