Long derided by critics as an inflexible ideologue, House Financial Services Chairman Jeb Hensarling is about to reach a major compromise to reauthorize the Terrorism Risk Insurance Act, potentially boosting his standing as he flexes his muscles in the next Congress.

In his first two years as chairman, the Texas Republican advanced a fiercely conservative agenda, showing little inclination toward conciliation. That’s changed over the past few days, as he closed in on an agreement with Senate Democrats to extend the government’s backstop of losses insured against terrorist attacks. The House is expected to vote this week on TRIA legislation that will draw support from both sides of the aisle and the business community.

Hensarling’s tenure has frequently been characterized by standoffs with Democrats, business groups and even House GOP leaders.

He advanced a bill through his committee last year to rewrite the housing finance system and eliminate mortgage giants Fannie Mae and Freddie Mac, but the measure was too controversial to get a floor vote. Amid a public outcry over higher flood-insurance premiums earlier this year, Hensarling refused to support some higher subsidies for homeowners, leading House leaders to sideline him on the matter.

Hensarling showed some willingness to take a half loaf, rather than a full one, in September; when he backed a leadership decision to reauthorize the Export-Import Bank for nine months rather than demand its outright expiration, as he had long pushed.

But he has moved furthest in the debate over TRIA. Last year, he publicly expressed skepticism with the program, which was enacted after the Sept. 11, 2001, attacks and remains popular in the business community and on both sides of the aisle. Hensarling later agreed to support legislation that would scale TRIA back, but the bill never won enough support among Republicans to receive a vote on the House floor.

Meanwhile, the Senate passed legislation with a whopping 93 votes, putting pressure on Hensarling to inch off his position, particularly as a Dec. 31 deadline to renew the program approached.

Hensarling and Sen. Charles E. Schumer, D-N.Y., met several times in recent weeks to try to bridge the gap, and Hensarling eventually dropped some of his biggest demands when it became clear they wouldn’t be accepted. That included a proposal to create a bifurcated system in which conventional attacks would be treated differently than nuclear, biological, chemical and radiological attacks. The final legislation is also not likely to have its costs offset, which Hensarling initially sought in negotiations.

The final compromise will raise the threshold to trigger the government backstop to a higher level of losses than the Senate proposed, but not as high as Hensarling had backed. And it splits the difference between the House and Senate on the length of the extension; the program will be renewed for six years, not the Senate’s seven nor the House’s five.

Conservative critics of House GOP leaders have floated Hensarling as a potential challenger to leadership, something he’s publicly considered. But in the latest standoff, he maintained the support of leadership from the beginning. One recent meeting between Hensarling, Schumer and House Majority Leader Kevin McCarthy, R-Calif., was largely intended to show that McCarthy had Hensarling’s back, congressional sources familiar with the discussions said. House Republicans were threatening to support a one-year extension as a fallback plan, something Schumer and industry groups opposed. After that meeting, momentum sped up toward a deal.

Even as news of the coming agreement was percolating, some Democrats were not convinced Hensarling would really embrace compromise.

“One thing that I do know is that I work with Mr. Hensarling, and he is unpredictable. And so you may hear one thing in this hour and another thing the next hour,” said Rep. Maxine Waters of California, the top Democrat on the Financial Services panel.

But if Hensarling gets TRIA over the finish line as expected, it will demonstrate a new willingness to bend and an ability to govern that he’s previously not shown. That will surely help him as he stakes out conservative ground and a higher profile in the next Congress.

Speaking of Hensarling’s TRIA negotiations, Martin DePoy, a lobbyist for business groups backing an extension, noted, “[He’s] come a long way.

Kate Ackley contributed to this report.