“When it comes to repealing Obamacare, what our members have talked about for years up here is going at the core of the law, which are changes to health-care spending that are mandatory,” says one senior GOP Senate aide.

McConnell does not have the authority to decide unilaterally that a given law can be repealed through reconciliation; instead, parliamentarians, the umpires of Senate procedure, interpret the relevant rules and precedents whenever a disagreement arises. Much of Obamacare does not qualify for reconciliation under the Byrd rule, the regulation that governs the process.

Some Republicans believe that McConnell has done more to deter colleagues from pushing for a full repeal than he did to convince the parliamentarians that it would be possible under the Byrd rule. “Internally, they’ve been aggressive in terms of, whenever this subject comes up, saying we can only do so much,” says one senior GOP Senate aide.