Merkel, invited to the White House to receive the Presidential Medal of Freedom, said Europe has a "vested interest" in ensuring the unrest in the Arab world doesn't spread across the Mediterranean Sea.
"The changes in North Africa are changes that happen on our doorstep," Merkel said.
"Those are our immediate neighbors and we have a choice. Either this works out well or we have an enormous refugee problem."
Germany abstained from voting on the U.N. Security Council resolution in March to intervene militarily in the Libyan conflict, adding to already lingering tension with the United States over the global economic crisis.
Sebastian Graefe, program director for foreign security policy at Heinrich Boell Stiftung, a German Green Party think tank in Washington, said the abstention "very much surprised" U.S. leaders. Graefe said Germany "is seen as a partner that's reactive."
"Right now the people we are talking with here in the U.S. are wondering what is the actual long-term policy in Berlin," he said.
At a news conference in the White House East Room, Obama and Merkel tried to clarify that policy. Obama said he expects "full and robust" support from Germany once the Gadhafi regime falls and praised Germany for providing relief troops in Afghanistan to allow other NATO allies to focus on Libya.
Both leaders said that Germany has a responsibility to help restore the Libyan people politically and economically. Merkel said Germany recently opened a facility in Benghazi that could be used to train security forces.
As a daytime flurry of bombs pummeled the Gadhafi compound and Tripoli, Obama pointed to recent high-profile political and military defections and a relatively free Benghazi as evidence of significant progress.
"What you're seeing across the country is an inexorable trend of the regime forces being pushed back, being incapacitated," Obama said.
Merkel agreed NATO forces are making significant progress and she pledged a more active German presence if Gadhafi is deposed.
"Germany is showing, will be showing, that it is responsible and committed to the Libyan cause. There will be a lot of problems still to contend with and we'll be in the closest possible contact," she said.
The German leader is the first European head of state to make an official state visit since Obama took office and the visit comes as a sign of continuity of U.S.-German relations, Merkel said.
"I appreciate those statements very much but we should be realistic," Graefe said of Obama calling Germany one of the strongest U.S. global allies.
"I'm not sure whether there's such a close cooperation between Germany and the U.S.," Graefe said. "I'm more skeptical."
Graefe said the Europeans believed Obama would strengthen trans-Atlantic relations but the 2009 U.N. Climate Change Conference in Copenhagen was a wake-up call because the United States focused on deals with emerging nations like China and Brazil rather than supporting the European Union.
Tuesday, Obama and Merkel talked about the "interdependence" of global financial markets but Merkel said solutions to economic issues begin at home.
"We in Europe have our hands full already with what we need to do and I'm absolutely convinced that as we shoulder our responsibility and meet our responsibility, so will the United States of America," Merkel said.
Graefe agreed Europeans need to define their own interests.
"Unfortunately even 21 years after the fall of the [Berlin] Wall we still look for the U.S., for Washington, to offer security to Europe," he said. "This needs to end. The Europeans need to take care of our own security by now."