Before the November election, House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) raged nearly every day against President Reagan, calling him unfit, a "cheerleader of selfishness" and a man with a "sinister" message.

Today, a much quieter O'Neill praises the president's arms control efforts, pledges to work "constructively" with the administration and tells the president, "In my 50 years of public life I've never seen a man more popular than you are with the American people."

O'Neill's conciliatory approach has been welcomed by the White House and by congressional Republicans. But there is ample reason to believe that the strongly partisan O'Neill may be biding his time to fight another day.

"He generally knows when to be the lion and when to be the fox," said O'Neill spokesman Christopher J. Matthews. "Right now he's the fox."

Said House Minority Leader Trent Lott: "It's a good political strategy -- it appears to be open and willing to cooperate. One thing Tip O'Neill is not, is dumb."

O'Neill's new tone is based in part on politics and the desire to have the Republicans take the blame for the unpopular measures being considered, including cutting student aid and veterans' benefits and possibly freezing Social Security benefit increases.

But associates said it also reflects a genuine respect for Reagan's electoral landslide and an uncertainty about where the Democrats need to go.

"I think he feels the president won 49 states and we have no right to say he's wrong. On the other hand it's not just that he's won but there is the belief that if he's allowed to go ahead he will overinterpret his mandate," one leadership official said.

Thus O'Neill would rather have the public focus on Reagan's proposals, at least initially, rather than Democratic attacks on them. For instance, Matthews said that O'Neill, who last year met the press every day the House was in session, may wait until after Reagan's Feb. 6 State of the Union address to resume that ritual.

"He feels strongly that there's going to be communication in the next three or four months between Reagan and the people, and the Democrats can't interfere with that," said one Democratic official. "It makes the water muddy to have a fight between Reagan and the Democrats. That's what happened in 1984 and that's why we didn't get our message across."

O'Neill adopted a similarly conciliatory tone after Reagan was elected in 1980, when Republicans and conservatives held more House seats than they do today.

Then, saying the new president deserved the opportunity to press his case, O'Neill put Reagan's program on a fast track. Much of Reagan's budget and tax program became law, and O'Neill and other moderate and liberal Democrats then used the "fairness" issue to go after Reagan and the Republicans.

When Democrats recouped nearly all their House losses in the 1982 elections, this strategy of giving the Republicans what they wanted so they would fall on their faces was given much of the credit.

Many House Democrats believe that allowing the Republicans to win in budget battles this year might lead to similar results in the 1986 House elections, particularly if the GOP ends up pushing a freeze on Social Security.

After a meeting with Reagan at the White House this week, O'Neill announced that the Democrats would not rule out Social Security revisions in any deficit-reduction effort but that such a move, like a tax increase, would have to be proposed by the Republicans.

O'Neill's recent low-key approach also reflects the introspection of the Democratic Party in the wake of the November election losses, Democratic officials said. That means being open to suggestions from the White House and others that in past years might never have been given a second thought.

For instance, agreeing to put Social Security on the table for deficit reductions this year would never have occurred a year ago, one O'Neill aide said.

"I think he feels it's time for a very sober assessment of where we go as a country and where we go as a party," Matthews said.

"There's no question that the speaker as a result of the 1984 elections . . . believes the party is seen as too weak on national defense, too viewed as tax-and-spend, and that there are programs on the domestic side that should be reviewed," said a close O'Neill associate.

In the meantime, Democrats and O'Neill have felt less pressured to jump into a debate over Reagan's budget proposals because of the renewed independence of House and, especially, Senate Republicans, who weeks ago began crafting their budget after the White House indicated that it could not achieve the deficit goals that the administration had set.

"It's a lot easier to sound conciliatory when the Republicans are going after the president's budget and talking about cutting defense," one Democrat said.

On top of all this, some O'Neill associates said, is a desire by the speaker, who has said he will retire after this two-year term, to end his tenure on a more upbeat note. That, too, means toning down the attacks.

O'Neill took a lot of pounding in the last few years. House Republicans accused him of being the most partisan speaker ever. And GOP candidates used him, and his wide girth and rumpled demeanor, as a metaphor for an out-of-shape, over-indulged, uncontrollable Democratic Party.

Reagan, who during the campaign once joked that he got his exercise by "jogging three times around Tip O'Neill," also has signaled a desire to tone things down.

According to O'Neill's aides, Reagan sent the speaker a friendly card on his birthday Dec. 9 and telephoned O'Neill in January when he was reelected speaker. And the two Irishmen last week apparently had one of the warmest meetings in more than a year.