Obama will need lawmakers to approve an ambassador and provide funds for an embassy.
The White House candidate said Obama has not made human rights a priority.
Senators, including Marco Rubio, Ted Cruz and Rand Paul, are asking for a plan by July 15.
Harriet Tubman was previously picked in an online poll to replace Andrew Jackson on the $20 bill.
The Republican presidential hopeful said Jerusalem should have a U.S. embassy before Havana.
The Republican leader added that a constitutional amendment likely wouldn't pass Congress.
The Florida Republican is the latest lawmaker to voice their concern over the talks.
He said Obama needs to “re-examine the point of the talks in the first place.”
Alexander Bolton 06/30/15 02:15 PM EDT
Sources close to McConnell say there's virtually no chance he will go along with the idea.
Sanders supports a constitutional amendment to undo the 2010 Citizens United decision.