The likely 2016 GOP candidate spoke out against Obama's move on Cuba.
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The move "sets an extremely dangerous precedent," Sen. Robert Menendez said.
Forty-seven percent have a favorable view, up 14 points since October.
The former Fla. governor faces a base hostile to his support for immigration reform.
The NBC/Wall Street Journal poll finds 71 percent want a different approach.
Obama offered Australia's leader help in the aftermath of a hostage crisis.
The first lady said her husband was mistaken for a waiter at a black-tie dinner.
"For Jeb Bush to run in the primary will be very, very difficult," the senator said.
She spoke out at a New York City gala against inequality.
The president met with his national security team to discuss possible dangers.