Although much banter and bear-hugging can be expected at a barbecue thrown by President Luiz Inacio Lula da Silva, several nagging issues surround them, from free trade to how to deal with leftist Venezuelan President Hugo Chavez.
"There is not a huge reserve of goodwill at the moment. It is so far off from a meaningful relationship," said Larry Birns, of the Washington-based Council on Hemispheric Affairs.
What the blue-blooded, conservative Bush and the leftist, former factory worker Lula appear to share right now is troubled times in their presidencies and waning popularity.
"One wounded president goes to visit another wounded president," Birns added.
Lula was feted at the White House when he visited in June 2003 and there was much talk of Brazil becoming the United States' leading ally in Latin America. But his government followed other paths and set out to become a regional power and voice for the world's poor countries.
"I think there were missed opportunities in the relationship. It's a pity," Brazil's former ambassador to the United States, Rubens Barbosa, told Reuters.
On the trade front, disputes over subsidies and market access caused the virtual collapse of a US-driven plan to create the Free Trade Area of the Americas.
Brazil also spearheaded a bloc of poor nations demanding more favourable farm trade rules in the Doha round of talks at the World Trade Organisation.
When US Deputy Secretary of State Robert Zoellick visited Brasilia last month, Brazil said it had asked the WTO for the right to impose trade sanctions against the United States because of an argument over cotton subsidies.
Zoellick criticised Brazil for pushing to open up agricultural markets while keeping its manufactured goods market protected. The relationship between the world's second and fourth largest democracies could be better, he said. Analysts say the United States needs Brazil to help keep the region stable as Latin America tilts to the political left.
Venezuela's President Chavez has proved tricky. Washington has decreed the populist leader a regional threat and wastes no opportunity to denounce him.
The United States had hoped that Lula, a friend of Chavez, would play a role in moderating his more radical tendencies. Yet only last month when Chavez visited Brazil, Lula praised him for the "excess of democracy" in Venezuela and worked to increase business ties with the oil exporter. With polls showing the actions of the Bush presidency have damaged US prestige in Latin America, Lula has been wary of the domestic political cost of following the US line.