ASHINGTON, Dec. 6 — "I'm a uniter, not a divider," Gov. George W. Bush of Texas never stopped saying during the presidential campaign, arguing that he could end the partisan gridlock of Washington.

The way his fellow Republicans on Capitol Hill are laying bare all their divisions, if Mr. Bush becomes president he may have to worry first about uniting Republicans before making deals with Democrats.

In the House today, Representative Tom DeLay of Texas, the majority whip, all but dared President Clinton to shut down the government in a fight over spending, a fight that Republicans have picked and lost before. Mr. DeLay's nominal superior, Speaker J. Dennis Hastert of Illinois, would plainly prefer to compromise with Mr. Clinton.

In the Senate on Tuesday, establishment conservatives held onto all the leadership positions, though the vote for policy committee chairman was only 26 to 24. That was not just an ideological test, though the loser, Senator Pete V. Domenici of New Mexico, is less conservative than the winner, Senator Larry E. Craig of Idaho, on issues like tax cuts.

Their other major difference, reflecting a fault line among the 50 Senate Republicans, is over how conciliatory to be toward the 50 Senate Democrats. Mr. Domenici is among the conciliators. Mr. Craig has said that with Dick Cheney available as vice president to cast tie-breaking votes, Republicans could look forward to being the majority that did not have to concede much.

It is not that Congressional Republicans do not want Mr. Bush to be president and to be a successful president. In both Houses, Republicans backed him, hoping he would win big and help them retain control. Mr. DeLay amiably hid himself from public view at golf courses during the Republican convention, but took a leading role in mobilizing staff "volunteers" to help out in Florida at everything from recount-watching to rowdy hassling of the Miami-Dade County canvassing board.

But now that they think Mr. Bush has won, their own political needs come first. And for veterans of years of tough fights with Democrats, the need to show no weakness comes ahead of creating any atmosphere of good will that might make it easier for Mr. Bush in dealing with a narrowly divided Congress.

Basically, Senate Republican leaders are talking as though the difference between the 54-46 Senate of this year and the 50-50 Senate they expect next year is a shift that alters committee ratios in a minor way, not something all but unique in Senate history. They may be posturing or taking an opening bargaining position they expect to abandon, but they do not sound that way.

A couple of weeks ago, the Senate majority leader, Trent Lott, told Robert Michel, the former House majority leader, that he could handle the likely 50-50 split by finding Democrats who would break with their party. And he spoke at Mr. Bush's Texas ranch on Saturday about handling the evenly divided Senate "very gingerly" and with the help of Mr. Cheney's vote. He predicted cooperation "from the Democrats."

But Mr. Lott has been as prickly about his prerogatives as any other Senate majority leader in many years, frequently using parliamentary devices to block Democrats from offering amendments. And while he may meet on Thursday with Senator Tom Daschle of South Dakota, the Democratic leader, to discuss what Mr. Daschle calls "power sharing," Mr. Lott told colleagues that he believed the Republican conference would never accept the idea of giving Democrats equal membership on a committee, even with a Republican chairman.

At least 4 of the 16 committee chairmen — Senators John McCain of Commerce, Richard G. Lugar of Agriculture, Jesse Helms of Foreign Relations and Mitch McConnell of Rules — have said they are open, with varying degrees of enthusiasm, to that kind of power sharing.

Some talk about it as a way to get things done. Without some accommodation, Mr. Lott's fellow-Mississippian Thad Cochran warned a few days ago: "I think it's going to be a challenge to get the Senate organized, given the 50-50 ratio that appears to be the destiny of the next Congress. If the Democrats wanted to be obstreperous, they could really make the Senate look leaderless."

Others point out that there is no way to be sure that a 50-50 Senate will remain that way. Not only are two old Republicans, Senators Strom Thurmond of South Carolina, 98, and Jesse Helms of North Carolina, 79, in less than great health, the Senate has seen much younger members die unexpectedly in recent years. So some Republicans argue that treating Democrats gently today may lead Democrats to be nice if they suddenly gain a majority.

In the House, along with the public wrangling over the spending, Mr. Hastert and his colleagues have a bunch of contested chairmanships to resolve. For the most part, these are contests of personal ambition, but a rejection of Representative Marge Roukema of New Jersey, the most senior Republican seeking the chairmanship of the Banking Committee, would be taken by many as a rejection of moderates and of women.

The House leaders are aware of that risk. But even more than their Senate colleagues, they must take into account a very conservative rank and file, many brought into Congress by Newt Gingrich not to get things done, but to get them undone or to prevent them from being done in the first place.