The official -- speaking on background and identified only as "senior" -- told reporters on Air Force One campaign officials think swing voters "responded well" to President Barack Obama's acceptance speech in Charlotte, N.C.
Republican presidential nominee Mitt Romney, campaigning in Iowa, said he read Obama's speech and found it "extraordinarily disappointing ... surprisingly disappointing, because [in] his speech four years ago he laid out a whole series of lofty goals and, unfortunately, he was unable to meet them."
"We think we had a terrific convention," the White House official told reporters. "We think it is going to help with turnout ... ."
The official said Republicans "came limping out of" their convention in Tampa, Fla., last week, without having "advanced the ball" for the Romney campaign.
"Our sense is in the electorate they did not make real progress," the official said.
The Gallup Daily tracking poll released Friday found Obama's job approval rating had improved to 52 percent, with his disapproval rating falling to 43 percent.
The administration official said Friday's Labor Department report that the economy added 96,000 jobs in August "reminds people of what they already know, the economy is healing but too slowly."
"We will see [what effect the report has on the campaign], the official said. "It is too early to know for sure."
Obama, campaigning in New Hampshire Friday, noted the economy has added jobs for 30 consecutive months but acknowledged "that's not good enough."
"We need to create more jobs, faster," he said, as he urged voters to pressure Congress to extend current income tax rates on all income under $250,000 and allow rates on income over that amount to rise as scheduled at the end of the year.