Washington — The White House has apparently plugged up some of the holes in congressional support for the United States marine role in Lebanon. House Republican leader Robert H. Michel, who had spoken earlier in his Illinois district of pulling American ground troops out of their Beirut airport position, emerged from a Washington briefing Wednesday with renewed optimism about events in Lebanon.
''There is some progress being made, and that is significant,'' said the GOP leader after national-security adviser Robert C. McFarlane met with House Republican leaders. Although he declined to give details, Representative Michel said he was ''satisfied'' with the administration's efforts to provide safety for the marines, a goal that he called uppermost in the minds of fellow House members.
Asked if that meant the White House intended to move the US troops, he said, ''They've always got their military position under review.''
Several hundred of the approximately 2,000 US ground troops are shuttled nightly to US Navy ships offshore since the terrorist attack on US marine barracks that killed 241 servicemen in October. The administration is considering moving even more of the marines offshore and possibly deploying some to safer positions south of Beirut, according to Pentagon sources.
Mr. Michel also said that he was convinced that the situation in Lebanon is improving, citing the strengthened, American-trained Lebanese Army as evidence.
However, the Republican leader noted a growing restlessness with the Reagan policy of keeping marines in Lebanon. While noting that his own Peoria, Ill., district has a big Lebanese community, he said, ''There could be any number of other districts in the country where people could care less about what happens to Lebanon.''
The apparently successful wooing of Michel came after Republican majority leader of the Senate Howard H. Baker Jr. (R) of Tennessee played down his doubts about Lebanon following a meeting Wednesday at the White House. Senator Baker told reporters that he expected no immediate change in the agreement which authorizes the troops to stay in Lebanon for up to 18 months.
The only exception to the apparent ''cease-fire'' of criticism among Republican leaders is Chairman Charles H. Percy of the Senate Foreign Relations Committee, who for the first time this week called for withdrawing the troops.
US forces should now ''rotate'' with troops from other nations that would not be targets for the warring factions in Lebanon, said the Illinois senator. He charged that the original mission of the marines as peacekeepers has now changed.
Democrats, meanwhile, are cautiously but steadily stepping up their opposition. With each day, as Congress nears its opening session Jan. 23, their protests are growing louder.
House Speaker Thomas P. O'Neill Jr., who had been a major supporter in winning the 18-month troop authorization for the Reagan administration, warned the White House to produce diplomatic gains soon or else face a reversal in Congress. After a meeting with his 15-member Democratic task force on Lebanon, the Massachusetts Democrat pronounced the ''status quo'' unacceptable. Although the Democrats were also briefed by administration officials this week, they argued that the officials offered no evidence of progress. One task force member , Rep. Augustus F. Hawkins (D) of California, wrote off the administration's explanations as ''fairy tales.''
Speaker O'Neill said he was hearing expressions of alarm from members of both parties, as the lawmakers report the concerns of their constituents back home. And minority leader Michel said he agreed that diplomatic progress is needed urgently.
However, Michel maintained that he could hold his Republican members in line with the White House if Congress were faced with a ''bring the troops home'' resolution when it returns.
That might be a difficult task. But at the least, the President is spared temporarily the public sniping from the top leaders of his own party.