Obama still leads Romney 51 percent to 45 in New Hampshire, but that’s down from the president’s 12-point lead in May. Obama leads by 3.5 points in New Hampshire, according to the Real Clear Politics average of polls.

Obama’s lead is buoyed by independents, who have tilted toward Romney nationally but go for Obama 52 to 40 percent in the Granite State.

New Hampshire is one of 12 battleground states that will be critical in determining the outcome of the 2012 election.

Romney launched his presidential bid and officially began his general election campaign in New Hampshire. He also owns a vacation house there and maintains close ties to the Granite State, which is near his home state of Massachusetts, where he served as governor. 

The PPP survey of 1,055 likely voters was conducted Aug. 9-12, partially before and partially after Romney announced Rep. Paul RyanPaul Davis RyanOn The Trail: Retirements offer window into House Democratic mood Stopping the next insurrection Former Sen. Bob Dole dies at 98 MORE (R-Wis.) as his running mate. The poll has a 3 percentage point margin of error.