MEXICO CITY — The sugar barons of Florida, Alfonso and José Fanjul, have been equal-opportunity political donors for decades, showering largess on the campaigns of Democrats and Republicans alike to ensure that lawmakers will protect the American sugar industry.

When Donald J. Trump was preparing to take office as president, the Fanjul brothers wrote another check. Among the contributors to Mr. Trump’s inaugural festivities in January was Florida Crystals, a Fanjul-owned company that contributed half a million dollars.

The brothers most likely had more on their mind than a sumptuous ball. Led by the Fanjuls, large American sugar producers and refiners were eager for the new administration to tackle some business left unfinished by the Obama administration: an agreement to control imports of Mexican sugar.

Now, with a Monday deadline for the United States and Mexico to settle on an accord, businesses on both sides of the border are watching to gauge what the sugar negotiations signal about Washington’s approach to renegotiating the North American Free Trade Agreement.