WASHINGTON (CNN) -- The Bush White House and the Republican National Committee are known for their consistent coordination of message. But when it comes to the latest flap over House Speaker Nancy Pelosi's alleged request for a military aircraft to take her home, the two GOP entities could not be further apart.

Some Republicans have taken issue with the size of the plane Pelosi requires to fly to her San Francisco district without stopping to refuel. The No. 3 House Republican, Rep. Adam Putnam of Florida, said Pelosi's desire for a large transport plane is "an extravagance of power that the taxpayers won't swallow."

As House Speaker, Pelosi is required to fly in a military aircraft, as was her predecessor, Dennis Hastert.

But White House spokeman Tony Snow took a different tact, telling reporters Thursday morning, "This is a silly story, and I think it's been unfair to the speaker."

Shortly after Snow's comments, the RNC fired off a press-release calling the California Democrat "non-stop Nancy" who is seeking a "flight of fancy."

When asked about the apparent disagreement between the White House and the RNC over the issue, Snow wouldn't comment besides reiterating the stance that "it is important for the speaker to have this kind of protection and travel."

Asked if the RNC is able to operate a media attack on its own, Snow quipped, "Well, they did this time."

As for Pelosi, on Thursday she again denied asking for a larger plane, and said a "myth" is out there about what she has requested. (Watch Pelosi respond to GOP critics)

Related: Pelosi will get plane, but not the one she wants

-- CNN Ticker Producer Alexander Mooney