In a memo to campaign leadership Monday, Matthew Dowd, Bush's chief strategist, said Kerry is about to benefit from "the average challenger's bounce."
"We should expect the race to swing wildly to his favor by early August," Dowd, who remains confident Bush will win, said in the memo.
Current polls show a dead heat, but Dowd said Kerry could be up by a 55 percent to 40 percent margin in early August.
Dowd also noted that Democratic National Committee chairman Terry McAuliffe predicted Sunday that Kerry would be up by 8 to 10 points following the convention.
Dowd told campaign officials that history shows a challenger always gets a "dramatic, if often short-lived" bounce from the convention and the selection of a running mate.
Speculation about Kerry's running mate has centered on Iowa Gov. Tom Vilsack, Missouri Rep. Dick Gephardt and North Carolina Sen. John Edwards as Kerry has kept mum about his preference. Kerry said last week the selection would be announced in an e-mail to supporters, but he would not say when it would go out. Others still in the mix as possible running mates include retired Gen. Wesley Clark, Sen. Evan Bayh of Indiana and Sen. Joe Biden of Delaware, though Biden downplayed his chances Monday.
"No one's done any vetting, any checking that I'm aware of," he told CNN outside his home in Wilmington, Del. "There's not a single thing that's occurred relative to the vice presidency and me that I'm aware of."
The Associated Press quoted two officials "close to the Kerry campaign" Monday who said that Edwards interrupted a trip to Walt Disney World last week to meet with Kerry in Washington.
But the officials cautioned about reading too much into that, saying Edwards is not the only potential vice presidential candidate who has met covertly with Kerry.
On Monday, Kerry picked up the endorsement of the National Education Association, the nation's largest union. The Massachusetts senator got 86.5 percent of the assembly's votes. Bush had declined to participate in the NEA's endorsement process.
Kerry will speak to the NEA convention on Tuesday.
"We believe John Kerry will work with educators to develop common-sense solutions to the challenges in America's classrooms, schools and communities," said Reg Weaver, NEA president.
The NEA endorsement means manpower and money in 15 battleground states targeted by the association.
Kerry on Monday hosted an Independence Day picnic near Pittsburgh that included supporters from Pennsylvania, Ohio and West Virginia, three November battleground states. The presumptive Democratic nominee will campaign in Pennsylvania, Indiana, Ohio, Wisconsin, New York and Washington, D.C., this week.
Bush, who will do a bus tour of Pennsylvania on Friday, had no public events on Monday. Instead, he went for a bike ride in Maryland. He was taken to a Secret Service facility in Beltsville, Maryland Md., for a bike ride.
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