WASHINGTON—When President Donald Trump addresses the U.S. agricultural community Monday, farmers will be looking for signs that a recent push to lobby him in support of the North American Free Trade Agreement has been successful.

That effort, which has included Republican senators from farm states offering charts and graphs illustrating the benefits of the trade deal, has left some hopeful that the administration has softened an earlier tough stance on Nafta. Fueling those hopes has been the president’s refraining from harsh...