McConnell does not have veto power As a senior citizen, I have had many opportunities to vote for a president, and I have not missed one. The president has the power to veto bills he or she does not agree with. I do not have, nor did I ever have, the opportunity to cast a vote on the election of Senate Majority Leader Mitch McConnell, yet he is, in effect, vetoing bipartisan bills passed by the House.