Obama insists it's not a conflict. "This is not an either-or question. This is a both-and question," he said earlier this month. "Fiscal stimulus is only one leg in the stool. We have to do financial regulation."
Led by Germany, many G-20 members oppose more government spending as a way to kick-start their economies.
"I think it highly unlikely that countries will press for or agree on a numerical figure for stimulus," says Dan Price, senior partner for global issues at Sidley Austin and former assistant to the president for international economic affairs in the Bush administration.
Rather than risk being turned down, Obama won't seek more stimulus now. "Nobody is asking any country to come to London to commit to do more right now," says Michael Froman, Price's successor. "There isn't any single number that is sacrosanct."
That could leave a boost in lending capacity for the International Monetary Fund as the summit's most concrete achievement. An increase of as much as $500 billion, as suggested by the Obama administration, would be used to help developing nations.
Choosing words carefully
Then it's on to a NATO conference along the French-German border, not far from where candidate Obama attracted more than 200,000 people in July. There he will try to convince allies of the wisdom of sending 21,000 additional U.S. troops and trainers to Afghanistan, on top of 62,000 U.S. and NATO troops already there.
Where Bush regularly pressed NATO for more troops, Obama appears ready to settle for trainers and civilian aid. That's despite increasingly difficult fighting in the country's southern and eastern regions.
"We are not in an easy situation, there is no doubt," German Ambassador to the U.S. Klaus Scharioth said last week.
In Prague, Obama will hold a summit with the European Union. There he will meet leaders who negotiated with the Bush administration for a U.S. missile-defense system in the Czech Republic and Poland that Obama has not committed to build.
Having dealt with the thorny issues he inherited, Obama also plans to raise others: climate change, cybersecurity, nuclear proliferation. He plans to give a speech on proliferation in Prague.
The trip is set to end in Turkey, a nation that is 99% Muslim but has direct ties to the West. "Turkey has always been viewed as a bridge between East and West, a kind of stabilizing influence in the region," says Ibrahim Hooper of the Council on American-Islamic Relations.
In his inaugural address, Obama pledged to seek a new relationship with the Muslim world "based on mutual interest and mutual respect." As a result, his every move and phrase in Ankara and Istanbul will be closely followed.
"The words will have to be chosen very carefully," says Bulent Aliriza, director of the Turkey Project at the Center for Strategic and International Studies.
Contributing: Ken Dilanian