WASHINGTON, July 28 — Two summers ago, on a Congressional trip to Estonia, Senator Hillary Rodham Clinton astonished her traveling companions by suggesting that the group do what one does in the Baltics: hold a vodka-drinking contest.

Delighted, the leader of the delegation, Senator John McCain, quickly agreed. The after-dinner drinks went so well — memories are a bit hazy on who drank how much — that Mr. McCain, an Arizona Republican, later told people how unexpectedly engaging he found Mrs. Clinton to be. “One of the guys” was the way he described Mrs. Clinton, a New York Democrat, to some Republican colleagues.

Mrs. Clinton and Mr. McCain went on to develop an amiable if professionally calculated relationship. They took more official trips together, including to Iraq. They worked together on the Senate Armed Services Committee and on the issue of global warming. They made a joint appearance last year on “Meet the Press,” interacting so congenially that the moderator, Tim Russert, joked about their forming a “fusion ticket.”

Politics being what it is, there is more friction than fusion. As the 2008 presidential campaign begins to take shape, with Mr. McCain and Mrs. Clinton at the top of the polls for their parties’ nominations, they are increasingly underscoring their differences on issues like the war in Iraq and port security. Advisers to Mr. McCain have put a stop to his inviting Mrs. Clinton on trips.