The Dow added a quarter of one percent, the S&P 500 rose a tenth and the Nasdaq climbed three tenths.
Fed Governor Christopher Waller said on Tuesday he is "increasingly confident" that the current level of central bank's policy rate is sufficiently restrictive and even hinted at the possibility of rate cuts in the months ahead.
And Chicago Fed President Austan Goolsbee touted progress in bringing inflation down.
But Fed Governor Michelle Bowman suggested another rake hike could be necessary to rein in inflation in a timely manner.
MarketVector Indexes Head of Product Management Joy Yang said she doesn't think the Fed will reduce interest rates anytime soon.
"My take is given like the resilience and what we've seen in some of these numbers, specifically the labor market, consumer spending, the economy itself. It seems like you know, we're not at the end of inflation, you know, until we see the labor market come down significantly, I think we're, you know, higher for longer."
Data out Tuesday showed consumer confidence surprised to the upside while the National Retail Federation said consumers plan to spend about five percent more during the holiday season this year.
Stocks on the move included Boeing, which climbed more than one percent after RBC Capital Markets upgraded shares from "sector perform" to "outperform."
Also, Micron Technology, which dropped nearly 2 percent after the chipmaker said it expects higher first-quarter operating expenses than previously forecast.