Senate and House Democrats have publicly backed Yellen in letters to the president, although both stopped short of opposing Summers as a nominee. And other liberal groups, particularly women's groups and financial reform advocates, have also grumbled about a Summers pick and are trying to tip the scales towards Yellen.
For his part, the president has defended Summers in public and private to Democratic colleagues but has not said he is a leading candidate to take over the central bank. He expects to make a nomination sometime this fall.
Trumka made clear he was not endorsing a candidate at this point, and that there was time for Summers to curry favor.
"He may come out and say, 'I am fully in favor of enforcing full employment as well as inflation.' If he's sincere about that … that's a different story," he said. "Until we get all the facts, I'm not going to make a decision and declare right here."
Trumka said that Fed presidents dating back to Paul Volcker under President Reagan have disproportionately emphasized controlling inflation over pursuing full employment when conducting monetary policy, even though the law requires it to pursue both goals. Trumka argued Yellen's track record makes her a better fit for the job.
"She's been very balanced in her approach forever. Not just last week, but forever," he said. "She's been right on predicting what's going to happen in the economy. I think those are important factors."