Republicans can rightfully exult in the brilliance of Karl Rove’s campaign and the success President Bush achieved in winning re-election by strengthening the Republican base and resisting advice to broaden his appeal.

That strategy enabled Bush to win a narrow but clear majority of Tuesday’s vote and cement the GOP’s hold on the White House and both houses of Congress.

But the message from voters went beyond endorsement of the Bush presidency. Many also suggested the president should re-examine some of his first-term policies and move toward the center in a way he failed to do four years ago.

The evidence is in the responses to questions buried in polling data.

Tuesday’s exit poll produced some questionable early numbers but did provide the best measure of voter attitudes and motivations.

The key question asked which came closest to their feelings about the Bush administration: angry, dissatisfied but angry, satisfied but not enthusiastic and enthusiastic.

Though Bush polled 51 percent of the vote, fewer than half of his voters said they were enthusiastic about his administration.

A late September poll asked whether, if Bush was re-elected, people wanted his second term to be similar or different from his first.

Just 9 percent said they wanted his second term to be like his first. An astonishing 58 percent said he should make major changes.

This suggests many voters want Bush to re-examine some of the policies that made his first term so controversial and helped to polarize the country.

The exit polls provided some elaboration: A clear majority felt Bush paid more attention to the interests of large corporations than to those of ordinary Americans and a larger proportion was very concerned about the availability and cost of health care.

Other questions showed voters overwhelmingly preferred Sen. John Kerry’s positions on Iraq, education, health care and the economy.

In his victory statement, Bush said the right things about reaching out to Kerry supporters. But the proof will be in the details. There are three areas in which he could change his approach:

• His often go-it-alone approach to global issues.
• His permissive attitude toward the budget deficit.
• His choices for key posts.

Personnel choices could provide an early clue. In forming his first administration, Bush paid only minimal heed to the sharp divisions reflected in his narrow victory and gave only the second-level post of transportation secretary to a Democrat.

But three factors minimize the chances of major changes:

• Bush does not easily admit error and might be disinclined to concede any errors in his first-term approach.
• Increased GOP strength on Capitol Hill improves chances for more conservative Bush initiatives and nominations.
• There is the natural inclination of any victor to see his success as vindication of his policies.

After the 1968 election, I was on a plane, seated behind John Mitchell, who had run Richard Nixon’s winning campaign, and a top adviser to the late Sen. Robert Kennedy.

The adviser was suggesting Nixon could have won a bigger victory. After listening for a few minutes, Mitchell leaned over and said, “We won, didn’t we?”

That’s generally been the attitude of presidents and their advisers, and it’s often produced no end of trouble. It’s more than likely to be the view Bush takes into his hard-won second term, but it may not be what his voters would like.