In the aftermath of the shutdown last month, business leaders from Washington and around the nation have vowed to play a greater role in coming primaries like this one.

They are increasingly concerned that a core group of anti-establishment conservatives in the House is threatening to derail their agenda, not just in terms of keeping the government open for business, but also when it comes to passing a comprehensive new immigration law, revising the nation’s tax code and making changes to the health care law, instead of just trying to kill it.

A second test case already emerging is in Michigan, where business groups are aligning behind Brian Ellis, a Grand Rapids investment manager who is trying to oust Representative Justin Amash, a Republican who was one of the core House lawmakers who supported the shutdown.

Mr. Byrne, who early in his political career was a Democrat before running as a Republican for state senator and then unsuccessfully for governor again as a Republican in 2010, clearly has the party establishment behind him. Two of the three congressmen who have held this House seat since 1965, two of the Republican candidates who lost in the September primary and the National Rifle Association have all endorsed him.

“We have a big choice to make and it’s an important choice, and if we make the wrong choice we can send somebody to Congress who’s a show horse and not a workhorse,” Mr. Byrne said at the debate on Wednesday night, presenting himself as a candidate who can make deals and get things done rather than pick fights on principle.

The Chamber of Commerce has contributed money in House Republican primaries before, but it expects to play a role in a greater number of these intraparty fights in the coming year.