Washington (CNN) Adam Schiff's profile is on the rise in Democratic politics -- but nobody seems to know what the California congressman will do next.

Until recently, Schiff was a well-regarded, but low-profile lawmaker in a Los Angeles market where he had to compete with two dozen other members of Congress for local media attention and 52 others for state-level press.

His post as the top Democrat on the House Intelligence Committee -- placing him at the center of the investigation into Russia's meddling in the 2016 presidential election and the potential involvement of President Donald Trump's campaign -- changed all that.

Now, Schiff is a day-to-day, hour-to-hour fixture on cable TV news. He earned a stop on the 2020 early-state speaking tour. And he even got a nickname -- albeit a recycled one -- from Trump: "Little Adam Schiff."

And his mocking response to Trump early this month got nearly 80,000 retweets. "Mr. President," Schiff wrote, "I see you've had a busy morning of 'Executive Time.' Instead of tweeting false smears, the American people would appreciate it if you turned off the TV and helped solve the funding crisis, protected Dreamers or...really anything else."

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