One crucial factor, governors said, is wooing independent voters who backed Mr. Obama last year but voted by about 2-to-1 margins in gubernatorial races for Robert McDonnell in Virginia and Chris Christie in New Jersey.
Mississippi Gov. Haley Barbour, chairman of the Republican Governors Association, told his colleagues that Obama enjoyed a “residuary of goodwill,” particularly because he is America’s first black president.
“We need to be careful,” Mr. Barbour said. “We need to treat the president respectfully….This is a guy that people like, but his policies are rightly dragging down their political capacity.”
Mr. Barbour’s comments underscored a challenge facing Republicans as conservative activists push the GOP to take a hard line in opposing the White House and, in some cases, Mr. Obama’s personal background.