Issa: Chaffetz stopped being a fighter
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Rep. Darrell IssaDarrell Edward IssaTrump to nominate retiring lawmaker as head of trade agency Overnight Energy: Watchdog to investigate EPA over Hurricane Harvey | Panel asks GAO to expand probe into sexual harassment in science | States sue over methane rules rollback Green group targets California GOP House candidates in new ads MORE (Calif.) on Friday had harsh words for his successor to lead the House Oversight Committee, Rep. Jason ChaffetzJason ChaffetzMatt Schlapp: Trump's policies on Russia 'two or three times tougher than anything' under Obama Tucker Carlson: Ruling class cares more about foreigners than their own people Fox's Kennedy chides Chaffetz on child migrants: 'I’m sure these mini rapists all have bombs strapped to their chests' 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 McCarthyOn The Money: Midterms to shake up House finance panel | Chamber chief says US not in trade war | Mulvaney moving CFPB unit out of DC | Conservatives frustrated over big spending bills Midterms to shake up top posts on House finance panel The Hill's Morning Report — Sponsored by United Against Nuclear Iran — Kavanaugh confirmation in sudden turmoil 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.