"We really would shock people if early in the evening of Nov. 6 it looked like Pennsylvania was going to come our way and actually did come our way. That can happen," Romney told about 200 donors who paid as much as $50,000 to attend his morning fundraiser.
Romney's visit - his first to the state in more than two months - is largely designed to raise the money needed to narrow Obama's edge in more competitive states. The campaign would not say how much it raised at the event, but he brought in $5 million at a Washington event Thursday and is expected to raise another $7 million at a Boston fundraiser later Friday.
"My priority is job creation and growing incomes," Romney told the donors. "My priority is not trying to punish people who have been successful."
Obama also will focus on raising cash Friday as he keeps his campaign close to Washington, where he has three fundraising events scheduled.
He is set to deliver remarks at a finance event at the Capital Hilton, where tickets start at $250 but go as high as $10,000 per couple. Obama will attend a smaller fundraiser at a private residence before returning to the Capitol Hilton for a third event.
On Thursday, Romney and Obama campaigned a few hundred miles apart in Virginia.
The president pledged to create many more jobs and "make the middle class secure again," while Romney focused on threats beyond American shores, accusing Obama of backing dangerous cuts in defense spending.
The Republican's message, including questions about the president's response to recent violence in Libya, comes as he tries to move beyond his long-held economic focus to help score political points and reverse a slide in the polls.
"The idea of cutting our military is unthinkable and devastating. And when I become president we will not," Romney declared at an American Legion hall in Springfield, Va.
He is expected to push a similar message on Friday in suburban Philadelphia during a rally at Valley Forge Military Academy and College.
The Pennsylvania GOP is set to begin running a television ad Friday assailing Obama's economic leadership. The state's unemployment rate, at 7.9 percent, is slightly less than the national average.
Obama and Romney are scheduled to face off Wednesday in Denver for the first of three presidential debates, which may represent the challenger's best remaining opportunity to change the trajectory of his campaign. Romney has struggled through a series of perceived missteps in recent weeks amid signs that confidence in the nation's economy is on the rise.
The Obama campaign released a political memo on Friday saying it expects Romney "to be a prepared, disciplined and aggressive debater."
However, it said that while the president would be laying out his vision for the coming years, Romney has "signaled that he will come to indict the president for the fact that the economy has not fully recovered from the collapse of 2008."
The Obama memo and an accompanying Web video also aim to debunk claims by Romney that the president has mischaracterized the Republican's positions on the auto industry bailout, abortion and raising taxes on wage earners to cover tax cuts for multimillionaires.
Obama was expected to meet with advisers Friday to prepare for next week's debate. The president was departing Sunday for Nevada, where he planned to hold debate practice sessions near Las Vegas.
Romney has been focused on fundraising and debate preparation for several weeks, raising some questions from within the GOP about his strategy. Earlier in the week, Romney said the time had come in the campaign when he would start spending less time with donors and more time with voters in swing states.
Obama campaign video: http://tinyurl.com/cllgnau
Associated Press writers Nedra Pickler, Jim Kuhnhenn and Ken Thomas in Washington contributed to this report.