Opponents of Philippine President Ferdinand Marcos, encouraged by reports that his government is struggling to stay in power, marched in front of the White House yesterday and called on President Reagan to back Marcos opposition leader Corazon Aquino.

"Reagan, don't miss the bus," shouted David M. Valderrama, a Prince George's County Orphan's Court judge and Filipino American, who addressed a rally in Lafayette Park before the march. "God almighty, don't miss the bus."

Speaking to about 300 demonstrators, Valderrama said various U.S.-based Filipino groups "are moving in the same direction" in challenging the "depraved and repulsive" Marcos government.

"We all know the dictator is falling," said Armin Alforque, a leader of a coalition of anti-Marcos groups that organized the protest. "The people have spoken: Marcos out now."

In a statement telephoned to the rally's sponsors and read to the demonstrators, Aquino said opposition to Marcos must be waged on several fronts at home and within the international community.

"Marcos is a formidable enemy who has built up an almost impenetrable power structure during his 20-year rule," Aquino said. " But if every single Filipino, both at home and abroad, does his bit, then there is no way Marcos can withstand the clamor for change . . . and genuine democracy."

The demonstrators frequently broke into chants of "Cory, Cory, Cory" during the rally. And they cheered reports from Manila that Marcos is encountering increased opposition, even from former supporters in the military.

" Jean-Claude Duvalier is out -- You're next, Marcos," read one sign, in a reference to the deposed Haitian president.

"We call on and encourage all Filipinos in the employ of the Philippine government, including employes of the embassy in Washington, to abandon the dictator Marcos and pledge their loyalty to the Filipino people in their new leader, Cory Aquino," said Gabby Lopez, a member of Kabayan, a Filipino human rights group.

A highlight of the rally was the appearance of Joy Villanueva, who delighted the demonstrators with her satirical impersonation of Imelda Marcos, the president's wife, who has often been criticized for her extravagant life style.

"Because of recent developments, my head is swimming with questions: What will I wear? Who will do my makeup?" said Villanueva.