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Sen. Chuck Grassley, the ranking Republican on the Senate Judiciary Committee, which will be the chief panel for many of Mr. Obama’s priorities such as gun control and immigration reform, also praised the president.

“I applaud him for his call for unity,” he said, though he added that part of that burden falls on the president. “He is going to have to quit dividing Americans between rich and poor.”

Democrats were enthused by Mr. Obama’s call to action — though Sen. Tom Harkin, Iowa Democrat and one of the chamber’s most liberal members, was asked whether the address was liberal enough for him.

He smiled and said, “It’s always kind of approaching it, never quite meets it.”