WASHINGTON (CNN) -- White House spokesman Tony Snow said Tuesday he doesn't think presidential politics is playing a large role in congress' reaction to President Bush's Iraq policy, even as likely presidential candidates jockey for a position on the issue as the 2008 campaign looms.

"Presidential politics obviously is going to grow larger in terms of its influence on the debate -- both with Iraq and domestic policy as we get toward end of the year and as we really get towards the primary season -- but at this point I don't think it's a huge factor," Snow told reporters during the White House daily briefing.

But given that eight potential presidential candidates sit on the major Senate committees likely to keep a close eye on the Bush Administration's new policy in Iraq, presidential politics may enter the fray sooner than the White House hopes.

Potential '08 rivals Sen. John McCain, R-Arizona, and Sen. Hillary Clinton, D-New York, each have a seat on the Senate Armed Services Committee.

Sen. Joe Biden of Delaware-- who has said repeatedly he's running for president -- chairs the Senate Foreign Relations Committee. Sen. Chris Dodd of Connecticut -- mounting a White House bid as well -- also sits on the committee along with potential contenders Sen. Barack Obama, D-Illinois, Sen. John Kerry, D-Massachusetts, and Sen. Chuck Hagel, R-Nebraska.

Sen. Sam Brownback of Kansas -- who plans to announce his intention to seek the 2008 GOP nomination Saturday -- holds a seat Appropriations Committee that oversees federal funding for the war.

Full White House Briefing