The Washington publication said it learned that the effort by a band of conservative House members was abandoned just a half-hour before last week's floor vote to re-elect the Ohio congressman to the top leadership post when they came up one vote shy of their 25-member goal.
While only 17 votes were needed to force a second ballot they hoped would lead to others joining them, the mutineers backed off when one unidentified member jumped ship, Roll Call said.
"There was an effort to get to a particular number," a Republican member who voted for Boehner but knew of the effort to overthrow him told the publication.
The rebel group's plan was to put forth a collection of names rather than a single person to avoid potential speaker candidates being pegged as instigators.
Roll Call said its sources said two senior Republicans the plotters hoped would emerge as leaders, Majority Leader Eric Cantor of Virginia and Financial Services Chairman Jeb Hensarling of Texas, had earlier refused to join in.
About half of the group either voted against Boehner or abstained, and Boehner, who has struggled to maintain cohesion among the various wings of his party through difficult budget negotiations, was re-elected.