Presidential political advisers anxious that the administration send a realistic budget to Capitol Hill have been citing surveys by pollster Richard Wirthlin showing that Ronald Reagan, even as his popularity declines, is still regarded as a strong leader by a majority of voters.

"Even those Americans who don't like where the president is leading us still think of him as a leader," one administration official said last week. "We're going to lose that if it looks like the Congress is forcing the president to behave responsibly."

Reagan strategists such as Sen. Paul Laxalt (R-Nev.), soon to be general chairman of the Republican National Committee, and Stu Spencer, manager of Reagan's 1980 presidential campaign, see an opportunity for the president to demonstrate his leadership quality by trimming the defense budget before Congress does it for him.

Some in the White House believe that Reagan would gain even more credit for demonstrating similar leadership on Social Security, although this is a more ticklish and difficult proposition.

But the pre-Christmas notion in the White House of sending up a budget that took a meat ax to social programs and a feather duster to defense is no longer politically appealing.

The new White House buzz phrases are "keeping the leadership edge" and "capturing the agenda," a task that some believe has been all but lost.

"The president to keep his leadership position must win some battles with Congress," one of his closest advisers said last week. "He can't do it passively and reactively by veto."

Another adviser says that if the president expects to run again he also can't wait for the budget battle to run its course on Capitol Hill.

"We have about 60 to 90 days to pull it out," he said.

The White House announced only that House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) didn't attend the bipartisan leadership dinner hosted by President Reagan last Monday night. What spokesman Larry Speakes didn't say was that O'Neill dropped in for cocktails beforehand, a courtesy that, as one White House staffer put it, "meant a lot to the president."

Still, White House hopes are pinned more on House Ways and Means Committee Chairman Dan Rostenkowski (D-Ill.) than on O'Neill. The favorable mention of Rostenkowski at Reagan's news conference last week was no accident.

Deputy chief of staff Michael K. Deaver had the best line at a senior staff meeting last week after chief of staff James A. Baker III explained that top administration executives didn't have to take the pay raise legislated by the lame-duck Congress unless they wanted to.

"Spoken like a true Houston multimillionaire," Deaver quipped.

Everyone laughed, including Baker. And the White House executives also took their raises.

Chrysler Corp. President Lee A. Iacocca was quick to respond to a White House trial balloon floated in this column last week suggesting that he become the new secretary of transportation. He called Deaver and said he wasn't interested in the idea, adding, "I wouldn't even want the job the president has."

The White House senior staff, led by Baker and personnel director Helene von Damm, then moved quickly to secure the appointment of Elizabeth Dole. They kept what they were doing such a secret that Dole, when she was summoned to the presidential residence at 4:45 p.m. on the day of her appointment, was instructed not to mention it in advance even to her husband, Sen. Robert J. Dole (R-Kan.). White House aides didn't want the appointment to leak on Capitol Hill.

White House spokesman Larry Speakes, trying to discourage reporters from writing about budget compromises before they happen, said at a briefing Wednesday: "This budget business is like starting to play Christmas carols before Thanksgiving. You get tired of them before Christmas."

When he wasn't fending off budget questions, Speakes was spending a lot of time on the telephone with White House counsel Fred Fielding seeking guidance on a spate of questions about conflicts of interest and reports that some government officials had used public funds for private travel.

Fielding, who takes seriously his job of enforcing government ethics, answered the questions but also told Speakes to deliver a personal message to the press corps.

"Tell them they're running me ragged," he said.

Idea of the Week: Recalling Reagan's solution to the unemployment problem--that every firm in America hire one jobless worker--a reporter on the president's fly-in to Louisiana to inspect flood damage came up with this proposal:

"If everyone on the trip would just take one bucket of water home and flush it down the toilet, we could solve the flooding problem."

And then there was the proposed bumper sticker for the hastily arranged extravaganza:

"He Cared Enough To Come To Louisiana (Briefly)."