LOS ANGELES — Early in Laura Poitras’s documentary “Citizenfour,” Edward J. Snowden, who exposed vast electronic surveillance by the United States government, tells what pushed him to go public.

“As I saw the promise of the Obama administration betrayed, and walked away from,” says Mr. Snowden, referring to drone strikes and invasive monitoring by the National Security Agency, “it really hardened me to action.”

But do some of President Obama’s staunch Hollywood supporters share his sentiment?

Her provocative, and deeply admiring, look at Mr. Snowden — which had its premiere at the New York Film Festival on Oct. 10 — arrived here this week amid high hopes, intense curiosity and more than a few raised eyebrows over its sharp critique of Mr. Obama, a president who has enjoyed strong support in the movie world.

The intrigue is especially pitched because several of the companies behind “Citizenfour” — which takes issue with Mr. Obama’s expansion of Bush-era surveillance, and his administration’s attempt to prosecute Mr. Snowden for espionage — are led by some of the president’s close political allies.