Washington — Domestic backing for US involvement in Lebanon appears to be crumbling fast as President Reagan returns to Washington to begin the new year. Democrats who until now have been quiet or supportive are breaking away, putting the Lebanon policy squarely into election-year politics. Democratic presidential front-runner Walter F. Mondale has broken his silence to call for immediate withdrawal of the US marines stationed in Beirut.
And fellow candidate Jesse Jackson dived directly into the Lebanon imbroglio, meeting with Syria's Hafez Assad to seek release of the captured Navy pilot, Lt. Robert Goodman Jr.
Meanwhile, three former Central Intelligence Agency chiefs called for pulling out the troops. And even Mr. Reagan's own Pentagon has sharply criticized the Lebanon operation.
The policy will face more criticism this week on Capitol Hill, where the kingpin in bipartisan support is wobbling and about to fall. Speaker Thomas P. O'Neill Jr. (D) of Massachusetts, the unlikely Reagan ally who assembled a House majority to keep the marines in Lebanon, is now said to have grave doubts. One aide describes him as ''on the verge of saying something really dramatic.''
So far the President has stood firm. ''In Lebanon the road to peace has proved long and hard, but there has been progress that would have been impossible without our marines and the other troops in the multinational peacekeeping forces,'' he said in a year-end radio address. It was the one sour note in an otherwise optimistic review of 1983.
A White House spokesman said Monday that there was ''no change'' and no expected announcement about Lebanon although the policy is ''a matter of continuing review.''
Speaker O'Neill's 16-member Lebanon task force, scheduled to meet today, will almost certainly send a loud warning to the White House that it wants changes. The Democratic panel, which has com-plained bitterly but largely unnoticed in past sessions, meets this week in the glare of publicity generated by the speaker.
The strategy is simple. O'Neill and fellow Democrats are alarmed by US bombing raids against the Syrians and the failure of diplomacy to extricate the marines from Lebanon. But they can't take action while Congress is in recess. Moreover, says an O'Neill adviser, ''I don't think the speaker would want to have Congress in a confrontation'' with the President.
Instead, the hope is to show President Reagan that support for the peacekeeping role in Lebanon is withering so that he will decide to remove the troops.
The apparent loss of Representative O'Neill's support is an important part of the message to the White House. During the acrimonious debates over Lebanon in September, the House speaker, arch foe of President Reagan in other areas, came to his defense and saved the day for the administration. O'Neill brought on board enough Democrats to pass a law permitting the marines to stay in Lebanon for up to 18 months.
In an emotional plea to his colleagues in September, the speaker said, ''I believe sincerely that the diplomatic efforts currently under way will not only promote reconciliation and stability in Lebanon, but I believe in my heart that it is going to mean an early departure of our marines.''
He also promised that he would ''personally monitor this situation'' and reserve the right to change his course.
That is apparently what he has now done. According to aides, his doubts about the policy stem mainly from the lack of diplomatic progress, the US air strike in December that stepped up the fighting, and concern for the safety of the marines as outlined in two new studies by a House subcommittee and the Pentagon.
''The speaker was led to believe it was going to be a short-term thing,'' says an O'Neill spokesman of the Lebanon involvement. ''He believes the administration has misread the situation there.''
''I'm somewhat surprised but pleased with his timing,'' says Rep. Pat Williams (D) of Montana, a member of the speaker's Lebanon task force, of O'Neill's reassessment. ''He believes the situation has reached a condition of alert, which is what we have been hearing in our briefings. The CIA has told us you can't protect those marines over there.''
Representative Williams, who voted for the 18-month authorization on the strength of O'Neill's plea, concedes that there is no easy way to bring the troops home. ''How do you get them out without endangering them and without giving terrorists an understanding that they drove us out?'' he says.
''It seems to me that we ought to go very slowly about (passing a withdrawal) resolution and should work quietly with the President and let him know that he only has a given amount of time,'' says Williams, who adds, ''I don't believe President Reagan wants to stand naked and alone on Lebanon.''
Republican leaders in Congress have also publicly raised questions about the policy in recent weeks. And, in telephone interviews, both Republican and Democratic members report growing concern among their constituents about Lebanon.
But while Congress is at home, it is still difficult to judge whether such reports will grow into a groundswell demanding withdrawal of the troops in Lebanon. O'Neill's rethinking points in that direction. But the White House still has at least until Jan. 23, when Congress reconvenes, to counter discontent with its policies.
''It isn't easy,'' said the President on Saturday of the US role in Lebanon. ''Progress is painfully slow, but progress is being made.''
President Reagan will probably have to provide lawmakers and other government officials more evidence of that progress or else see most of his support slip away.