The Public Policy Poll, conducted among 900 U.S. voters April 12-15, shows Obama leading Romney 49-46.
Members of each party are rallying around their candidate, with the president's support among Democrats up 5 percent in the past month -- from 79 percent to 84 percent. Romney's support among Republicans has risen 4 percent, from 78 percent to 82 percent, the poll showed.
"As expected, Republicans are consolidating around Romney as Democrats rally to Obama," said Dean Debnam, president of Public Policy Polling.
A choice by Romney of Chris Christie as GOP running mate would result in a 47 percentage point tie as well as the tightest national popular vote, the poll found.
Conversely, the poll found having 2008 Republican vice presidential nominee Sarah Palin as a running mate this year would hurt Romney's chances, with An Obama-Biden ticket soundly beating Romney-Palin 50-43.
The margin of error for the survey was 3.3 percentage points.
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