Bush will seek to ease relations with Putin during their Kennebunkport "lobster summit" -- a reference to the local specialty cuisine.
But many observers are skeptical the two leaders can bridge the growing divide between themselves and their two countries.
Marshall Goldman, a professor emeritus of Russian economics at Wellesley College in the U.S. state of Massachusetts and author of an upcoming book on Putin's energy policy, said that the disagreements are too strong for that.
"I don't have high expectations, because I think the issues that now separate the two countries cannot be settled in two days, even if it's a nice, informal, warm two days between the two leaders," Goldman said.
No Common Ground
Putin has regularly criticized what he calls U.S. efforts to dominate the world, while Bush has denounced the state of democracy in Russia under Putin.
Russia particularly sees a planned U.S. missile defense system in Poland and the Czech Republic as a threat. Washington, however, insists that the system is targeted at possible attacks from "rogue states" such as Iran.
Moscow and Washington are also at odds over the future of the Serb breakaway province of Kosovo. Putin opposes Western efforts to allow Kosovo to move toward independence from Serbia under UN supervision.
Russia and the United States have also never agreed on how to approach Iran's nuclear program, with Washington favoring sanctions and Moscow refusing to take a harsh stance.
Goldman said Bush is making an effort to show that he isn't "losing" Russia:
"What I think Bush is trying to do is to make one last effort to show that indeed, he can deal with Putin and that indeed, he has not lost Russia," Goldman said. "I think that Bush recognizes that if he doesn't make this extra effort, that's indeed what people will say: "Bush came in with Russian relations pretty good and left with Russian relations pretty bad. You, President George W. Bush, lost Russia." I think he wants to avoid exactly that kind of criticism by doing this kind of thing. I think that's what motivates his efforts."
Anne Applebaum, a columnist for the "The Washington Post" newspaper and a regular commentator on Russia, agreed.
"You know the way Bush understands politics," Applebaum said. He probably feels that at some point in the past, he had a good relationship with Mr. Putin on a personal level. And he wants to try revive that in order to make things better between Russia and the United States. I mean, it's actually a fairly naive view of politics."
Kennebunkport, one of Maine's chic coastal tourist towns, is expecting protesters today, demonstrating against Bush, the Iraq war, and Russia's policy toward Chechnya.
(RFE/RL correspondents Yury Zhigalkin and Irina Lagunina contributed to this