No Republicans were willing to speak critically of Boehner on the record, and even among those who are critical of his strategy, he remains very popular.
But privately, numerous lawmakers and veteran GOP operatives acknowledged a growing division within the conference over Boehner's focus on a big deal.
"It's failed twice. Twice ... get over it," one rank-and-file Member said recently, pointing to Boehner's failed negotiations with Obama this summer and the failed super committee talks this fall.
A second Republican Member agreed, saying Members are increasingly frustrated that Boehner has focused so much on finding a massive win to the detriment of smaller potential victories.
"We're in a terrible position to get anything big done," this lawmaker said, explaining that part of the frustration stems from the looming elections and nervousness among Members about getting things such as a change to the defense sequester done.
"The closer we get to election season, the more people look to home" and want to get accomplishments under their belt, the Republican said.
Others, including Latham, dismissed those concerns, arguing that Boehner is simply dealing with the reality that sweeping systemic changes are needed to fix the economy and the federal budget.
"He knows it's what has to be done for the country," Latham said.
Boehner supporters also discounted the notion that his focus on the big picture has cost Republicans anything.
Boehner has been successful in getting "the best possible deal that he could for conservatives and has generally run the table on the president all year," Holt argued. "At each step along the way, he's established a basic conservative principle going into resolving" these issues.
"His caucus has pushed him and he's responded by profoundly changing the conversation in Washington," he added.
A review of this year's legislative accomplishments bears that out. With earmarks banned — one of Boehner's biggest accomplishments before even taking the speakership — the appropriations process has shifted from an annual fight over how to spend money to how best to cut spending. Even Democrats such as Minority Leader Nancy Pelosi (Calif.) have adopted the rhetoric of deficit control and spending constraints, long the providence of fiscal hawks in the GOP.
Under Boehner, Republicans have also forced Democrats and the White House to agree to more than $1 trillion in spending reductions over the next decade, and the discussion on Medicare and Social Security has shifted from whether to reform the programs to how best to reform them.
But despite those successes, frustration with his approach continues to build, particularly over his decision not to try to modify this summer's debt deal "sequester" to reduce its effect on defense spending.
Boehner himself acknowledged that some of his Members, particularly the freshmen, have been disappointed at the pace of success. "Our freshmen over the last couple of weeks have been in this grouchy mood," he said during Wednesday's event at the Newseum.
In fact, that frustration with Boehner's approach has risen to the level that Majority Leader Eric Cantor (Va.) openly broke with the Speaker in an exchange with Minority Whip Steny Hoyer (D-Md.) on the floor earlier this month.
Sen. Jeff Flake, R-Ariz., takes a selfie with his cut-out head during the Hoops for Youth 16th annual charity basketball game held at George Washington University's Smith Center, September 8, 2014. The members of Congress team beat the lobbyist team 46-40. Buy photo here.