Sentence:  Under this approach, a <WSD>superminority</WSD> of 34 Senators could prevent a sole executive agreement from enjoying the full force of the supremacy clause vis-a-vis state laws. 
Meaning of the word marked with <WSD> tags:  A voting block which, although it has less than 50% of the vote, has sufficient numbers to prevent any other group from forming a supermajority.