Issa: Chaffetz stopped being a fighter
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Rep. Darrell IssaDarrell Edward IssaThe Hill's 12:30 Report On The Money: New York AG sues to dissolve Trump Foundation | Issa tamps down rumors of consumer agency nomination | Bank regulator faces backlash over comments on racism | Cohn contradicts Trump on trade Issa tamps down rumors of consumer bureau nomination MORE (Calif.) on Friday had harsh words for his successor to lead the House Oversight Committee, Rep. Jason ChaffetzJason ChaffetzChaffetz knocks Sessions: He's 'the attorney general in name only' Chaplain controversy shifts spotlight to rising GOP star Ingraham’s ratings spike a wake-up for advertisers MORE (Utah), as the two Republicans eye the Speaker's gavel.

"Look, Jason is a good man, an honorable man, but he got his job by going to Boehner and saying he would shut down that rancor that was going on, he would go along, get along — and he's done that; he put shining pictures of Utah on the wall — and he basically stopped doing it," Issa said during an appearance on MSNBC's "Morning Joe."

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Issa was alluding to Chaffetz, in one of his first acts after taking over the Oversight gavel early this year, removing portraits of Issa and other past chairmen from the committee's hearing room. Chaffetz said at the time he and others wanted to be inspired "by those we serve."

"He's a good guy, but whatever he was as a freshman, when he was a fighter on our committee, when he trying to hold government accountable — he took a break from that," Issa said.

Issa is himself considering running for Speaker, The Hill reported Thursday, pitting him against Chaffetz and Rep. Dan Webster (R-Fla.), the only Republicans who have declared their intension to run.

Republicans are also putting pressure on Rep. Paul Ryan (R-Wis.) to run for the position after Majority Leader Kevin McCarthyKevin Owen McCarthyHillicon Valley: Trump hits China with massive tech tariffs | Facebook meets with GOP leaders over bias allegations | Judge sends Manafort to jail ahead of trial | AT&T completes Time Warner purchase McCarthy: 'The Mueller investigation has got to stop' McConnell: Mueller 'ought to wrap it up' MORE (R-Calif.) abruptly dropped out of the race on Thursday.

Issa suggested Friday that he may be among those who should be considered for Speaker should a "consensus candidate" such as Ryan not materialize. Ryan, the one-time vice presidential nominee, has said he doesn't want to run.

"I am considering whether or not to put my name in the hat," Issa said during another morning show appearance on CNBC's "Squawk Box."

"To be honest, I probably am better suited to be the Republican leader or committee chairman," he said. "It's a question of, can we come together, can we get our broad party together [on issues]."

Contrasting himself from Chaffetz, Issa suggested on MSNBC he wouldn't have the "hubris" to determine if himself or someone else would be popular enough to become the next Speaker.