There will be plenty of opportunities to achieve bipartisan success on pro-growth initiatives such as trade, immigration, education reform, tax reform, and efforts to reign in the deficit. There will also be constant pressure on the president and Republicans in Congress to put their differences aside and deliver more accomplishments such as the tax deal, he said.

Tackling the deficit

Mitchell said Obama's efforts to move to the middle will take a major initiative, such as tackling government spending by closing or shrinking government agencies.

McConaghy said that as voters are concerned about government spending and the size of the federal deficit, Obama can take aggressive action on the report proposed by the deficit commission.

The deficit commission is a panel responsible for recommending where and how to make cutbacks in a bid to reign in the ballooning U.S. deficit.

Obama's economic challenge

The economy looms large over the president and Congress, and is likely to remain the most important issue to Americans.

The Nation, on its blog, noted that no president in more than 50 years has ever been re-elected when the unemployment rate stood above 8 percent.

That could spell trouble for the president, since economists predict that the unemployment rate, which stands at 9.8 percent, will lower at a snail's pace over the next several years, and some even forecast that it will not hit 8 percent until 2013.

"I suspect at the end of the day what really is going to matter for Obama in 2012 is the economy," Mitchell said. "If we still have unemployment anywhere close to 9 percent, that's not going to be a good situation for him, even if he's successful in trying to rebrand himself as a moderate."

But despite a weak economy, there does not, at least now, seem to be a Republican candidate who could beat Obama, some experts said.

Could Obama turn to foreign policy?

Because U.S. presidents tend to be weak midway through their first term, and because domestic policy is so rancorous, foreign policy is ironically one of the only places where a president can make a splash, some experts contend.

Still, that may be part of Obama's playbook, said Scott Payne, policy adviser for national security at Third Way.

In spite of Obama's win with the START ratification, the current state of the world does not appear to lend itself in the near future to the victories that have helped Obama, he said.

Afghanistan remains difficult, the Middle East peace process is moving slowly, and the situation on the Korean peninsula remains tense. These are not issues that appear likely to give President Obama easy wins in the near future, said Payne.