The Senate’s passage of a tax overhaul illustrated a fragile coalition of support that ironically provides the chamber with the upper hand headed into conference committee negotiations with the House.

House Republicans wanted a conference process on the two chambers’ differing tax bills to prevent the House from getting jammed by the Senate, as they acknowledge has happened frequently on major bills.

But some members realize that a conference committee may still result in a final product that tracks more with Senate priorities given the thin margin of support in that chamber.

Senate passage came after days of negotiations in which several Senate Republican holdouts were offered significant concessions to secure their votes, with some changes designed just to appease a single senator.

“You have senators over there negotiating 400 billion things. That’s why people want to be in the Senate, not in the House,” Pennsylvania GOP Rep. Ryan A. Costello said, acknowledging that the Senate “absolutely” has the upper hand heading into conference.