Expectations that U.S. Treasury Secretary John Snow (search) would survive President Bush's Cabinet make-over for at least six months are rapidly yielding to a belief he may make a hastier exit, people close to the Bush administration said on Thursday.

Some sources said Snow could stay on for another month or two but likely not much longer.

Asked about the rising speculation, Snow told Fox News on Friday: "That's a matter for the president and me to discuss."

"It is an honor to be part of this administration," Snow also told Fox News' Neil Cavuto on Your World. "I have been very pleased to be part of this administration."

White House chief of staff Andrew Card (search) was among those cited as a possible replacement for Snow if he leaves. Other names floated were former Sen. Phil Gramm (search), U.S. Trade Representative Robert Zoellick (search) and White House budget chief Joshua Bolten (search).

Some Republicans, however, said Bolten would stay in his current job or possibly succeed Card as chief of staff if Card were to go to Treasury.

The large number of names bandied about added to a sense the top economic job might be in play sooner than thought.

One Republican close to the administration saw Card as the most likely choice, saying that in addition to his ties to Bush, Card has a good rapport with members of Congress and with Federal Reserve Chairman Alan Greenspan (search).

"The Greenspan blessing is key here," the source said. "He's the president's man. He shapes policy. He sells policy and he gets things done."

For the moment, interest centered on the drama of Snow, who took the Treasury helm in early 2003 after predecessor Paul O'Neill (search) angrily resigned after breaking with the White House over tax cuts.

The 65-year-old Snow traversed the country in the election campaign to praise Bush's tax cuts and tout economic growth. After the Nov. 2 election, most had expected he would be allowed to leave gracefully within six to 12 months, without a push.

Many Republicans said the administration dropped a not-so-subtle hint about Snow's future on Monday when an unnamed official was quoted in the Washington Post as saying the Treasury chief could stay as long as he wants "provided it is not very long."

"If the attribution of that quote is to a White House official, it's clearly a shot across the bow to Snow," said William Niskanen, head of the Cato Institute think tank. "It makes one very cynical about the way Washington operates."

Many administration officials were aghast at the tone of the comment, especially since Snow, a lawyer, economist and past chief of rail freight giant CSX Corp. (CSX), has been a tireless cheerleader for Bush's policies.

The White House had ample opportunity to squelch the speculation. But when asked by reporters whether the Post report was accurate, spokesman Scott McClellan refused to discuss speculation and said only that President Bush "appreciates the job Secretary Snow is doing."

The Treasury job achieved its pinnacle of distinction when Robert Rubin held it during the Clinton administration.

Some judgments offered about Treasury's role in the Bush years, under O'Neill and Snow, were harsh.

"It's been an empty chair for the last four years," said Republican strategist Scott Reed.

The White House might feel it needs a fresh slate of players to push Social Security and tax reform in Congress and to set overall priorities, said economist Douglas Lee of Economics from Washington.

"There is a feeling among many people that Treasury is not ready to move forward on tax reform proposals yet and there is some dissatisfaction with that," Lee said. "I haven't heard of anyone who says that they have been bowled over or greatly impressed by Secretary Snow."

Snow has won credit for picking up the baton at Treasury after O'Neill's abrupt departure and avoiding the verbal gaffes that tarnished his predecessor's tenure.

"Snow is not a lot of glitter and gold ... but he's been quite effective and quietly loyal to Bush," said Stephen Moore, president of the conservative group Club for Growth.

Reuters contributed to this report.