In a sign of just how sensitive the topic has become for Republicans, neither Corker nor Lankford has publicly detailed how their proposal would work—despite the fact that Senate leaders plan to amend and pass their far-reaching bill as early as Thursday. And while conservatives are trying to ensure a trigger stays out of the measure, they aren’t yet threatening to abandon legislation Republicans desperately want to enact. During a meeting of House Republicans on Wednesday morning, according to a senior GOP aide, party leaders urged rank-and-file members not to criticize the emerging Senate bill until after it passes the upper chamber. In exchange, House members were assured they’d have the opportunity to fight for changes in a conference committee to reconcile the two bodies’ competing bills.

Conservative lawmakers in both chambers are instead pushing for a mechanism that would trigger automatic spending cuts rather than tax increases, although that might be even harder to pass through the Senate. And the Senate bill would already set off cuts to Medicare that Congress may quickly try to undo.

Trying to head off a conservative revolt, Lankford has been talking for weeks about a possible trigger with his former colleagues in the House, where he served for four years before moving to the Senate. The Senate plan, like a House bill approved earlier this month, would reduce the corporate tax rate to 20 percent from 35 percent. Under one proposal floated by Lankford, that rate would rise to 21 percent after five years if the economy doesn’t grow at a fast enough clip.

Some GOP senators are uneasy with even that modest change. “Personally, I don’t support triggers,” Nevada’s Dean Heller said at a Wednesday press conference. Senator Thom Tillis of North Carolina argued that the mere threat of a future tax increase would discourage businesses from taking advantage of the lower taxes to begin with. “The perverse consequence of having a trigger in here could potentially be that we won’t achieve the economic gains that we would otherwise have if the trigger were not,” he said.

For now, the trigger debate isn’t a deal breaker for many Republican senators, who don’t want to jeopardize the broader tax bill over a provision that might not survive the legislative process. Republicans can’t lose more than two of their members and pass the bill. Corker and Lankford have each drawn a hard line on the issue to this point, and Senators Jeff Flake and John McCain of Arizona have voiced similar concerns about the bill. “I don’t want to see this bill destroyed because of a pursuit for perfection,” Senator David Perdue of Georgia said.

The trigger mechanism could run afoul of the Senate’s budget rules, analysts have said, causing the provision to be stripped out before a final vote. Or it could be watered down in negotiations with the House to a point where conservatives don’t see it as an actual threat to their tax cuts. The decision would then swing back to the deficit hawks, who would face tremendous pressure not to topple a landmark Republican bill at the very last moment.