The enthusiasm with which conservative congressional Republicans greeted President Bush during his State of the Union speech concealed for a night the differences that threaten his proposals for Social Security and immigration reform.

Those divisions have been strikingly evident in the weeks leading up to Wednesday night’s speech and will be even more apparent as Congress considers the president’s proposals.

But another, less visible split within the GOP could well come to the fore in the coming years as moderate Republicans, long overshadowed by the dominant conservatives, flex their muscles in the campaign to choose the party’s next presidential nominee.

Signs of that impending battle were evident last August when some conservatives groused that such prominent party moderates as former New York Mayor Rudy Giuliani, California Gov. Arnold Schwarzenegger and Arizona Sen. John McCain got the best speaking slots at the Republican convention.

Now, a new book by former New Jersey Gov. Christie Whitman argues that unless Republicans resume some of their moderate stances, they could lose their majority status.

In one sense, the argument by the woman who was Bush’s first head of the Environmental Protection Agency revolves around the question of whether he won re-election because of or in spite of his administration’s strongly conservative tenor.

“President Bush’s victory has led many to conclude that the best way for the Republicans to win is by targeting the base,” Whitman writes in “It’s My Party Too.” But she adds, “It could just as easily be true that the president’s win was only the latest in a long line of victories by incumbent commanders in chief during times of war.

“So before the Republican Party institutionalizes the politics of making the red states redder and ignoring the rest of the country, it might decide whether it believes that true political leadership is best advanced by further dividing the nation in pursuit of electoral victories.

“I believe pursuing such a course would be a profound mistake,” she concludes. “It would not only present a very real danger to the party’s continued ability to win elections; it would also call into question whether the party is in fact worthy of governing the United States of America.”

Whitman, who was often overruled by White House conservatives while at the EPA, accuses the GOP right wing of “tearing our party and our country further and further apart” by taking “doctrinaire positions on a handful of key issues, including abortion, stem cell research and marriage.”

While this has enabled the Republicans to win national power “with the slimmest margin of victory,” she says, a broadened appeal to moderates would help it become “a true majority party.”

She notes that moderate Republicans — herself and Tom Kean — won four of five New Jersey gubernatorial elections between 1981 and 1997. But the GOP lost in 2001 with a more conservative standard-bearer.

It’s impossible to say whether a more moderate Bush would have won by a bigger margin in 2004. But it seems clear that her point will get a good test in 2008.

The party’s presidential field could include several prominent moderates — McCain, Giuliani and outgoing Homeland Security Secretary Tom Ridge.

They differ some on abortion rights and on issues such as a constitutional ban on gay marriages. All will probably draw opposition from conservative groups, which are more likely to back Sens. Bill Frist of Tennessee, George Allen of Virginia, Sam Brownback of Kansas, Rick Santorum of Pennsylvania, or Gov. Jeb Bush of Florida.

Conventional wisdom says a McCain or a Giuliani can’t win in today’s conservative GOP. The 2008 nomination battle may well answer that question.

The role of party moderates could also be important in the shorter run, because there are enough in the Senate to undercut the GOP’s 55-seat majority.

For now, however, Bush’s main domestic political concern will be whether he can win the votes of those conservative Republicans who cheered so enthusiastically on Wednesday night.