Thomson Reuters

Opponents of change include Sen. Robert Menendez, a Cuban-American from New Jersey who is chairman of the Democratic Senatorial Campaign Committee.

The strength of feelings on both sides will make it a "challenge" to get Congress to go farther than Obama did on Monday, said Jake Colvin, vice president for global trade issues at the National Foreign Trade Council, which represents major U.S. exporting companies.

Still, at least some believe U.S. policy has reached a tipping point, even if it is still some time before the embargo is ended.

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