The S&P 500 was modestly higher and the Nasdaq more solidly in the black. The blue-chip Dow was lower, with all three indexes losing steam in mid-afternoon trading.
A spate of data, including jobless claims and consumer spending, suggested that the plodding economic recovery could be losing steam.
But in the latest development in negotiations for a new pandemic relief deal, the White House countered House Democrats' $2.2 trillion package with a $1.5 trillion-plus proposal, to include a $20 billion aid extension for airlines.
U.S. House Speaker Nancy Pelosi cautioned that Democrats and the White House remained locked in a debate over dollars an values, but expressed optimism that a deal could be reached.
"The market is viewing the stimulus as a lubricant for the economy, to take the market to the next level and to keep the consumer strong," said Matthew Keator, managing partner in the Keator Group, a wealth management firm in Lenox, Massachusetts.
"One of the encouraging things is the Speaker and the Treasury Secretary (Steven Mnuchin) have kept an open mind, which leads to the adage 'hope springs eternal.'" Keator added.
The major stock indexes started the fourth quarter with gains driven again by market leaders such as Amazon.com, Microsoft Corp and Apple Inc .
The Dow Jones Industrial Average fell 82.41 points, or 0.3%, to 27,699.29, the S&P 500 gained 2.26 points, or 0.07%, to 3,365.26 and the Nasdaq Composite added 101.83 points, or 0.91%, to 11,269.33.
Of the 11 major sectors in the S&P 500, communications services was the largest percentage gainer, while energy companies lagged the most.
With the books closed on the third quarter, market participants await earnings season, set to get underway in about two weeks.
Analysts currently see S&P 500 earnings, in aggregate, falling by 21.4% year-on-year according to Refinitiv.0.3
Exxon Mobil Corp dropped 3.8% after it signaled a bigger-than-expected third quarter loss as falling oil costs and plunging demand.
Boeing Co rose 0.4% and after Federal Aviation Administration Chief Steve Dickson remarked "I liked what I saw" following Wednesday's 737 MAX test flight.
Advancing issues outnumbered declining ones on the NYSE by a 1.58-to-1 ratio; on Nasdaq, a 1.33-to-1 ratio favored advancers.
The S&P 500 posted 11 new 52-week highs and no new lows; the Nasdaq Composite recorded 60 new highs and 34 new lows.
By Stephen Culp