THE new team running the White House and the Bush campaign signals an opening up of the small, tight circle of power around the president.Already, since he was named the new White House chief of staff Thursday, Samuel Skinner has been stressing his openness to all options for reinvigorating the economy - vowing to "leave no stone unturned, no good idea ignored." His message is that the White House is ready to act because the economy is now clearly not reviving as once expected. The White House has been at a loss to communicate a clear direction on the economy. Yet Mr. Bush's reelection prospects rest largely on the confidence people retain in the economy and his ability to manage it during the next 10 months. Those familiar with Mr. Skinner's style expect to see him consult more widely and delegate more responsibility to staff than did outgoing chief of staff John Sununu, an intimidating, dominating presence who held responsibility closely. Mr. Sununu showed every intention of holding close control of the Bush campaign as well. His departure, and the makeup of the new campaign team, signal to Republican strategists that the clout has shifted from the White House staff to the campaign staff. The character of the people involved also indicates a better chance that the two staffs will not battle each other to control the President's time and message. The new team also has raised some uncertainties. One is who will play the role of the late Lee Atwater, the scrappy, street-smart strategist who managed the Bush campaign in 1988. Mr. Atwater was valued not just for his hard-edged campaign attacks but for his sense of how to appeal to middle- and working-class white voters. This is the common touch that the White House has sometimes conspicuously lacked. The campaign chairman and strategist is Robert Teeter, a veteran pollster and consultant with an even temper and moderate Republican politics. Like most of the campaign team, Republican consultants call him "incredibly smooth," competent, and "a consensus builder." The Atwater touch is more likely to come from two senior advisers to the Bush campaign, Charles Black, a former Atwater associate who earned his political spurs with North Carolina Sen. Jesse Helms (R); and Richard Bond, a longtime Bush operative from Long Island. Republican strategist Eddie Mahe says that Mr. Bond is "every bit of what Lee Atwater was as a man of the street. "If he were not there, I'd be worried about that," Mr. Mahe says. Another Republican and former White House official calls Mr. Black "probably the most effective one in the campaign or the White House to communicate a message." Still another Republican strategist, however, is concerned that if the President is embattled in 1992 and his campaign needs a hard edge, the campaign leaders will shy away from it. "That's not what these guys like to do," the strategist says. Also of concern is that the campaign may in fact need some of what Mr. Sununu would have brought - the willingness to make fast, difficult decisions and bear their brunt. "Campaigns function too fast anymore to be run by people not willing to take hits," says the Republican strategist. The campaign will face difficult tests very early on because of the candidacies of David Duke and Pat Buchanan, not because either is a serious threat the Bush nomination but because they are not. Both will be on the attack, trying to pick up delegates, with little to lose. "It's very hard to defend against suicide missions," says the strategist. Sununu had the position and the temperament to act fast and authoritatively. Power is spread thinner now. The general chairman and lead fund-raiser will be Robert Mosbacher, the current secretary of commerce and a Bush friend since their days as young oil men in Houston. The campaign manager, Fred Malek, has an outstanding reputation as a manager who can make the trains run on time, but his reputation was sullied as a hatchet man in the Nixon White House. Some are wondering who can make decisions that stick in this environment. Mr. Teeter and Mr. Mosbacher can certainly go directly to the president with their views. So can Skinner, of course, as chief of staff, although he is not likely to have as much control over White House business as Sununu exercised. Skinner has not yet indicated how extensively he will bring in his own team to the White House staff. He reportedly gets along well with Mr. Darman, whose Office of Management and Budget has attained tight control of domestic policy in the administration. With the budget summit of 1990, then the Gulf war, the shaping of policy grew increasingly concentrated in the hands of just a few top officials. The White House has always been especially careful to avoid raising expectations on domestic policy, wary of creating momentum it cannot brake. Skinner is now arguing that the "baton has been passed" from the foreign policy team to the domestic policy team, which is ready for action.