Story highlights Boehner has been speaker since 2011 and has said he's not going anywhere

Hensarling says he's flattered by the attention, but is not thinking about being speaker

But he's leaving the door open as some conservatives have been unhappy with Boehner's leadership

Some conservatives unhappy with House Speaker John Boehner 's leadership are looking for a replacement, and recent moves by Texas Republican Jeb Hensarling are fueling speculation he wants Boehner's job in the next Congress.

Hensarling, who was part of Boehner's leadership team two years ago but left to chair the House Financial Services Committee, gave an expansive speech last week hosted by Heritage Action for America, a group that frequently and publicly clashes with Boehner.

Asked afterward if he was interested in running for speaker, Hensarling initially said he was "flattered," and said, "It's not something I've aspired to. It's not something I'm thinking about."

But then he left the door open, saying, "No, I haven't been Shermanesque, again I'm not sure there's any opportunity I want to foreclose."

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Photos: John Boehner's political career Photos: John Boehner's political career John Boehner has been the speaker of the U.S. House of Representatives since 2011, making him second in line for the presidency, behind the vice president. On September 25, Boehner told colleagues he's stepping down as speaker and will leave Congress at the end of October. Look back at his career in politics so far. Hide Caption 1 of 23 Photos: John Boehner's political career Pope Francis walks with Speaker Boehner and Vice President Joe Biden after delivering a speech to Congress in Washington on September 24. Hide Caption 2 of 23 Photos: John Boehner's political career Afghanistan President Ashraf Ghani (right) expresses his country's gratitude for America's fiscal commitment and military sacrifices during an address to a joint meeting of the United States Congress with Vice President Joe Biden (left) and Speaker of the House John Boehner (R-OH) in the House Chamber of the U.S. Capitol March 25 in Washington. Hide Caption 3 of 23 Photos: John Boehner's political career U.S. President Barack Obama walks with Speaker of the House John Boehner as they depart the annual Friend's of Ireland luncheon on Capitol Hill in Washington on March 17. Hide Caption 4 of 23 Photos: John Boehner's political career U.S. Vice President Joe Biden and Speaker of the House John Boehner await the arrival of President Barack Obama for the State of The Union address on January 20 in the House Chamber of the Capitol. Hide Caption 5 of 23 Photos: John Boehner's political career The image of the Speaker of the House John Boehner (R-OH) is displayed in a monitor of a camera as he talks with reporters in his office in the Capitol in November 2014 in Washington. Hide Caption 6 of 23 Photos: John Boehner's political career Boehner blasts conservative groups during a press conference in December 2013 after passing a compromise budget deal aimed at removing the threat of another government shutdown. Fed up with criticism from conservative advocates, Boehner said they were "misleading their followers." He followed up with: "Frankly, I just think that they've lost all credibility." Hide Caption 7 of 23 Photos: John Boehner's political career Reporters question Boehner as he arrives at the U.S. Capitol as the government stalemate continued in October 2013. President Obama signed a bill on October 17 that ended the 16-day shutdown and raised the debt ceiling. Hide Caption 8 of 23 Photos: John Boehner's political career Boehner speaks to the media after a meeting with President Obama at the White House in October 2013, the second day of the federal government's recent shutdown. The White House squared off with Republican rivals in Congress over how to fund federal agencies, many of which were forced to close, leaving a fragile economy at risk. Hide Caption 9 of 23 Photos: John Boehner's political career Boehner is sworn in as the speaker of the House after his re-election in January 2013. Hide Caption 10 of 23 Photos: John Boehner's political career Boehner presents golfing legend Arnold Palmer with the Congressional Gold Medal at a special ceremony in the Rotunda of the Capitol in September 2012. Hide Caption 11 of 23 Photos: John Boehner's political career On January 5, 2011, Boehner wipes away tears as he waits to receive the gavel from outgoing House Speaker Nancy Pelosi, D-California, during the first session of the 112th Congress. Hide Caption 12 of 23 Photos: John Boehner's political career Boehner hugs his wife, Debbie, after addressing the crowd at the NRCC Election Night watch party on November 2, 2010, when Republicans took back control of the House of Representatives. Boehner met his wife in college, and they have been married since 1973. Hide Caption 13 of 23 Photos: John Boehner's political career Boehner voices his concerns about the health care reform bill championed by Obama during a news conference in Washington on October 29, 2009. Hide Caption 14 of 23 Photos: John Boehner's political career Boehner, an avid golfer, talks with Tiger Woods while golfing at the Congressional Country Club in Bethesda, Maryland, in 2009. Hide Caption 15 of 23 Photos: John Boehner's political career Boehner, center, looks on as President Barack Obama speaks with then-House Majority Leader Steny Hoyer in the East Room of the White House on February 23, 2009. Boehner and Obama have butted heads over the years. Hide Caption 16 of 23 Photos: John Boehner's political career Boehner, center, and fellow Republican House members sing Boehner's birthday song during a news conference on Capitol Hill on November 17, 2006. Boehner served as the House Minority Leader from 2007 to 2011. Hide Caption 17 of 23 Photos: John Boehner's political career Boehner answers questions during an interview with Bloomberg in Washington on June 29, 2005. Hide Caption 18 of 23 Photos: John Boehner's political career President George W. Bush signs into law the federal education bill No Child Left Behind at a high school in Hamilton, Ohio, in 2002. The law offered the promise of improved schools for the nation's poor and minority children and better-prepared students in a competitive world. Boehner, second from right, backed the bill. Hide Caption 19 of 23 Photos: John Boehner's political career Boehner and House Majority Leader Dick Armey, R-Texas, listen to House Speaker Newt Gingrich at a 1997 news conference with entrepreneurs promoting the GOP tax relief plan. Hide Caption 20 of 23 Photos: John Boehner's political career Boehner dumps out coal, which he called a Christmas gift to President Clinton, during a news conference about the federal budget on December 21, 1995. Many government services and agencies were closed at the end of 1995 and beginning of 1996 as a Republican-led Congress battled Clinton over spending levels. Hide Caption 21 of 23 Photos: John Boehner's political career Boehner at a Capitol Hill news conference on February 6, 1995. He has had a seat in the U.S. House of Representatives since 1990. Before that he was a member of the Ohio State House of Representatives for six years. Hide Caption 22 of 23 Photos: John Boehner's political career Boehner, R-Ohio, holds a copy of the Constitution on Capitol Hill in Washington on May 7, 1992, as Sen. Don Nickles, D-Oklahoma, looks on. Both men proclaimed it was a historic day when the Michigan House ratified the 27th Amendment to the Constitution, which would require that any Congressional pay raises not go into effect until after the next election. Hide Caption 23 of 23

While Heritage Action's Chief Executive Officer Michael Needham told CNN that his group doesn't get involved in leadership races, the conservative group gave Hensarling a high-profile platform to outline his own conservative philosophy for governing.

Needham said there is a "real need to take on sacred cows in Washington at time when the party too often looks after K Street," a reference to the downtown D.C. address for corporate lobbyists. He said, "Jeb Hensarling is a great spokesman and fighter for conservative values."

Boehner has said he's staying put

Boehner, in his 12th term in Congress and in his second as speaker, continues to insist he's not going anywhere and expects to remain in charge next year. But he raised questions earlier this month when he wouldn't commit to serving out another full term as speaker.

At the beginning of the current Congress in January 2013, a dozen House GOP members voted for someone other than Boehner, or voted "present," an expression of no confidence. Many in that small group are convinced Boehner won't run for his post after this year's midterms or that he won't have the votes to keep that title.

If Boehner decides to step down from the position, House Majority Leader Eric Cantor is popular among conservatives, and most expect him to move up and take the speaker's gavel. In that scenario conservatives could wage an effort to fill in top House GOP posts.

Multiple House Republicans -- some who voted for Boehner in 2013 and some who didn't -- praised Hensarling as a solid conservative, but also told CNN there's a short list of others who are viable candidates.

Many House Republicans interviewed by CNN declined to talk openly about potential leadership challenges, but admitted there are informal discussions about options.

The names repeatedly raised include Ohio Republican Jim Jordan, who like Hensarling is a former chairman of the fiscally conservative Republican Study Committee; Louisiana Republican Rep. Steve Scalise, who currently heads that group; and Georgia Rep. Tom Price, another former study group leader who also served in Boehner's leadership team in the last Congress.

"The one consensus point is that we'd like to see more conservatives in future leadership posts," Louisiana Republican John Fleming told CNN.

But he cautioned for now there's no single alternative emerging to Boehner -- or anyone who might want to challenge the speaker's current top lieutenants -- Cantor and GOP Whip Kevin McCarthy. He said he expected more serious discussions to ramp up by the end of the summer.

Hensarling's recent speech at Heritage may be a way to ensure his name gets in the mix. The Texas Republican used the speech to position himself firmly on the right. He called out his own party for breaking with its free market roots, arguing that the party should be shifting away from policies designed to help big business and the well-connected and instead champion policies to help the "Main Street competitive economy."

The thrust of Hensarling's speech lines up with the message many on the right flank of the House GOP conference have been pushing. Idaho Republican Raul Labrador has publicly criticized House GOP leaders for pushing a legislative agenda that positions the GOP as the "party of big business" and doesn't resonate with small businesses and entrepreneurs.

Challenging the party

Hensarling argued those on Main Street are "not looking for a subsidy, earmark, tax preference or legislated advantage."

On a series of issues -- tax reform, farm policy, reform of mortgage giants Freddie Mac and Fannie Mae -- Hensarling challenged his party to hold votes on legislation that would restructure current federal systems.

The bulk of Hensarling's ire was directed at the Export Import Bank, the 80-year-old credit agency that gives out loans to companies to promote U.S. exports. The bank's lending authority is due to expire at the end of the year.

Hensarling held it up as the poster child of corporate welfare, citing that the vast majority of its taxpayer backed loans go to companies like aircraft manufacturing giant Boeing. He said getting rid of the bank "is a defining issue for our party and our movement."

If Hensarling or anyone else is serious about mounting a challenge, the Republicans that CNN interviewed all agree that if they are serious they need to move soon.

"It seems to me that the odds of there being some type of change within the leadership team seem to be more likely than less, and so as long as there are members talking about it it's better to do so early than late," Iowa Republican Rep. Steve King told CNN.

North Carolina Republican Rep. Walter Jones, who opposed Boehner in the last election, told CNN that he hears from Republicans in his district that it's time for a leadership change in Washington.

"There is a great deal of frustration," Jones said.

He wasn't sure if Hensarling or someone else was the right fit, but said a successful campaign required several months or preparation.

A few months ago unhappiness about Boehner's handling of government spending fights and concern he would negotiate with Democrats on a major immigration bill roiled the conference. But because members aren't coalescing around a single alternative, the vacuum gives Boehner some job security for now.

Fleming said tension is down between conservatives and Boehner because the speaker agreed to form a select committee on the deadly Benghazi terror attack and hold a House vote that held former IRS official Lois Lerner in contempt for the controversy around her agency's targeting of conservative groups.

He said "there are less things that divide us -- but the one question would be immigration."