But Swonk said the Fed is caught in a difficult spot, and there are good reasons why it would want to ease sooner even though it's unlikely.
"It's the Fed's conundrum. ... The markets are pricing in easing infinity. If they raise rates, they could destabilize the markets. If they don't raise rates, they're feeding a bubble. It's a hard place to be in," she said.
Barclays' chief U.S. economist, Michael Gapen, is among a minority on Wall Street who believe the Fed could raise rates in September.
"I hope she steps up and gives an interesting speech. Don't give me this blah-dity blah. The markets need to hear from her. She's lost some credibility with investors. There are many market participants that believe she will never see sufficient data to make her move," he said
Gapen said Yellen should sound a bit more hawkish and more confident in the economy when she speaks, but he agrees that the Fed chair can't give the nod to a September hike because of the pending August jobs report, released the following Friday.
But he expects that report to confirm the recent solid trend, clearing the way for a hike. Gapen said the Fed could even slip in a second increase at the end of the year.
"I can see a world where that happens. I can also see a world where it doesn't. In my view, they need to be opportunistic when they have the window on good news. The good news it the labor markets have rebounded and the recession is not there as some have feared," he said.
Wednesday's release of Fed minutes somewhat put to rest heightened speculation that the Fed could raise rates in September, a time frame that was written off by many on Wall Street because of the mixed performance of the economy and the proximity to the presidential election.
In the lull of a mid-August market, talk had picked up after comments Tuesday from New York Fed President William Dudley, who basically warned the market it is too complacent and that it would be appropriate for Fed to hike soon, maybe even at its September meeting.
But the Fed's minutes from its July meeting showed a divided central bank, with some members too worried about the economy while others were ready to raise rates. The Street took that release as meaning the Fed remains in dovish mode even though the views reflected in it were three weeks old. Treasury yields fell and the dollar resumed its downward trajectory, as the market moved back to the view that the only hike this year would be in December.
"Listen to Dudley and not the minutes," wrote Deutsche Bank currency strategist Alan Ruskin. "I think Dudley could not have been clearer on the (market) being mispriced on Fed rate risks. If you take the FOMC minute headlines at face value, the slightly softer 2yr yield that followed the minutes is the correct response. However, I expect the rates/FX market will go back to focusing primarily on the latest read from Dudley."
The opinion of Dudley is important since he is viewed as close to Yellen, at the center of the dovish core of the Fed. So it was important that when speaking to the press Thursday, he doubled down on his earlier comments.
"My views haven't changed since Tuesday," Dudley said to reporters. He also said growth is picking up in the second half and that the labor market is continuing to improve. On the labor front, he also said there are some signs that wages are picking up and there has been a turnaround in hiring of jobs in the middle of the scale, after several years of growth only in the lowest- and highest-paying jobs.
Swonk said Dudley has to be worried about the buoyancy of financial markets, since as the head of the New York Fed he is the official most closely tied to the markets. She said it would be hard for the Fed to move in September, with the heightened uncertainty surrounding this year's election.
"It would just put them in a political hail storm for no reason," Swonk said. "There's a good economic policy reason to delay past the election. Talk about making yourself a political pinata. It looks like you're turning a blind eye on one of the most contentious election cycles we've ever had. You've got to be cautious."
Gapen said the election could end up being a factor to stay the Fed.
"It's possible but I think I'd say on a first-order basis, they do things irrespective of the political calendar. But they're people too and they don't want to be a part of the debate. If anything, the fact there's an election out there probably makes them more sensitive," he said.
Gapen added they could see a move in September as a way to get ahead of the election. "If she's dead set on going in September, she has to give a pretty clear speech. The volatility tends to be driven by unexpected things. If you're worried your move is going to generate volatility, just be clear about what you're going to do. Let markets get there and then you can make your move."