"He relinquished the power of the purse, and with it he lost my vote," Oklahoma Congressman Jim Bridenstine said in a statement, titled "I Will Not Vote for John Boehner" Friday.
Bridenstine claims that Boehner's $1.1 trillion short-term government funding deal with US President Barack Obama "went too far", adding that the deal "sufficiently undermines the checks and balances enshrined in the Constitution".
"I've already said I cannot vote in good conscience for John Boehner," Jones stated in a local North Carolina radio interview before Christmas.
The Republican Congressman added that he had been meeting "with a small group" of "about 16, 18" other Congressmen who are prepared to name a different Speaker when the vote takes place next week.
A new US House speaker will be chosen on Tuesday, January 6, on the first day of the 114th session of Congress. So far, no alternative candidate has been named by Boehner's opponents.
In December, the House of Representatives passed the $1.1 trillion spending bill just hours before the US government's spending authority was due to expire. Republicans were reluctant to vote for the bill, as they were dissatisfied with Obama's executive action on immigration.