Speaker John A. Boehner and Majority Leader Eric Cantor could be in for another showdown with Heritage Action for America.

One day after the chamber’s top two Republicans endorsed authorizing U.S. military intervention in Syria, the influential conservative advocacy group has come out in opposition.

“Heritage Action is opposed to punitive missile strikes on the Syrian regime. Yesterday’s hearing made it clear there is not a vital U.S. interest at stake,” said Heritage Action spokesman Dan Holler in a statement Wednesday morning. “Further, there is not a clear, achievable, realistic purpose to the use of force being contemplated by the Obama administration and officials offered little evidence such action would prevent further abuses.”

At this point, Heritage Action doesn’t appear to be designating legislative action on the resolution to authorize military force against the Syrian government as a “key vote.” Its key vote list, used to rate members’ loyalty to the conservative cause, is often the most powerful weapon in its arsenal of tactics to compel members to hew to their line.

But the group still holds considerable sway over the right wing of the House Republican Conference at a time when every vote is being counted for next week’s highly anticipated roll calls in the House and Senate.

The organization has taken credit for many of House GOP leadership’s legislative catastrophes over the past year, most notably on the farm bill.