Federal Reserve Chair Janet Yellen faces the biggest public challenge of her brief tenure when she delivers a speech at the central bank's annual pow-wow in Jackson Hole, Wyoming on Friday. And, millions of Americans' jobs weigh in the balance of how well she can steer her peers' policy decisions.

Yellen more than her predecessors, has called on the central bank to respond forcefully to high joblessness by keeping borrowing costs low, arguing that inflation isn’t likely to surge in this weakened economy just yet. When she speaks for the first time Friday at the Fed’s, she will need to support her view with evidence. If she’s right and doesn’t convince her colleagues, more Americans will lose their jobs or give up job searching.

She's spoken unusually frankly and personally on unemployment, a trait rare among central bankers. In a speech in February, 2013, when Yellen was the Fed's Vice Chair, serving under Ben Bernanke, she said in a speech, 

These are not just statistics to me. We know that long-term unemployment is devastating to workers and their families. Longer spells of unemployment raise the risk of homelessness and have been a factor contributing to the foreclosure crisis. When you're unemployed for six months or a year, it is hard to qualify for a lease, so even the option of relocating to find a job is often off the table. The toll is simply terrible on the mental and physical health of workers, on their marriages, and on their children.

It's also worth noting she used the word 'inflation' just nine times in that speech. She used the word 'unemployment' 36 times.

If the Fed believes the economy’s growth and hiring will pick up and inflation will rise to a normal 2 percent, the central bank would likely pull back further on its easy money policies, purchasing government bonds to keep stock prices up, and may hike the interest rate it authorizes banks to charge each other for lending, raising borrowing costs for consumers on everything from homes to cars. But if the Fed overestimates the economy’s strength and pulls back too soon, it would halt an already weak housing recovery and send unemployment skyrocketing.

Yellen, arguably the most powerful woman in the financial world, has focused her academic career on unemployment trends and has forecasted the U.S. economy more accurately than any other Fed official from 2009 to 2013, according to a Wall Street Journal analysis. In 2009, she and others predicted the Fed’s easy money policies wouldn’t push inflation dangerously high, and so far, they have been right.

The Fed released minutes of its late July meeting on Thursday, showing the policymakers have moved a bit closer to raising interest rates, though they still haven’t reached a consensus. Yellen’s speech is needed to show how much the Fed has moved its stance, so global markets and financial policymakers will parse Yellen’s every word for a hint of the Fed’s next step.

“There is a growing debate as to whether the Fed should follow its current course of supporting growth with low interest rates or whether it should begin to tighten to slow the economy and keep the unemployment rate from falling much further,” said Dean Baker, co-director of the Center for Economic and Policy Research. “The inflation hawks will be trying to push the case that the labor market is getting tight and that the Fed needs to act soon, if not now, to head off inflation. Yellen needs to make the case that we are very far from a situation in which inflation would be a problem and there is plenty of time before the Fed needs to do anything.”

In July, Yellen told Congress that if the labor market continues to improve more quickly than anticipated by the Federal Open Market Committee (FOMC), that makes decisions about interest rates and the growth of the U.S. money supply, then higher interest rates would “likely occur sooner and be more rapid than currently envisioned.” The Committee has the tools it needs to raise short-term interest rates “when the time is right,” she said.

At a press conference in June, she had made clear that time wasn’t here yet, citing unemployment that though falling doesn’t wholly represent a tightening labor market, a market that would raise wages faster than inflation. Americans’ wages are currently creeping upward at about the same pace as overall price increases, which in July came in below expectations, according to recent Labor Department data.

“Until this broad evidence (specifically – clearly accelerating wage and price inflation) shows that the economic slack created by the Great Recession has been absorbed, she will keep providing substantial monetary boost to the economy through low rates,” said Josh Bivens, director of the Economic Policy Institute. “And, the benefits of continuing to try to boost economic activity and jobs far outweigh the risks of possible future inflation.”

“The only hiking talk will be on the trails,” economists at Bank of America Merrill Lynch analysts wrote in an August research note, describing their view that Yellen won’t shift the Fed’s policy at the meeting.

Yellen’s leadership is widely seen as a continuation of her predecessor Ben Bernanke’s reign, but one difference between Yellen and Bernanke is that Yellen has been explicit in expressing her concerns about asset bubbles. In her July testimony, Yellen said investors were over-valuing junk bonds, a type of risky, high-yield bond, forcing investors who held them to re-examine their positions. Since then, yields for junk bonds have risen substantially.

“This latter policy, which I have long advocated, is an effort to use the Fed's enormous stature in the financial world to bring pressure to bear on bubbles,” Baker said.

In the past, as with former chair Alan Greenspan, the Fed has sat complacent with bubbles, then tried to mitigate the mess when they burst with extended low interest rates. That worked in 2001 during a mild recession but not the Great Recession in 2008. Market watchers coined the strategy the “Greenspan put” and then the “Bernanke put,” begging the question now whether there will or should be a “Yellen put.”

“Overall, a lot still depends on whether or not wage growth accelerates as the labor market continues to improve,” said Paul Dales, U.S. economist for Capital Economics. As of Thursday, he forecasts an interest rate hike in March 2015.