WASHINGTON — There were about 30, all Mexican nationals desperate to avoid deportations that would separate them from their families. Living in Illinois, they appealed for help from their new U.S. senator, Barack Obama.

He turned them down.

It was one of the first times Obama could have used the power of his office to help defer the removal of immigrants who were in the United States illegally. Eight years later, with his powers magnified as president, such a decision is upon him again, this time with the status of millions of immigrants at stake.

That episode in 2006 represents just one early marker in Obama’s complicated history with the politics of immigration. The son of a Kenyan immigrant, Obama has been embraced and scorned by immigrant advocates who have viewed him as both a champion and an obstacle to their cause.

Now, perhaps paradoxically, in their anger over his delay of executive actions that potentially could give work permits to millions of immigrants living illegally in this country, these advocacy groups also hold out hope that when Obama does act, he will be aggressive and leave a mark for posterity.