Bullard, who is not a voting member of the policy-setting FOMC this year, won't vote again until 2016.
"This has been the great debate taking place in the market: When will the normalisation of policy begin?" Henk Potts, a strategist at Barclays Wealth & Investment Management in London, told Bloomberg News. "The Fed is starting to give clues about what the exit strategy will look like. What investors should really be focused on is not when the rate rise comes through, but the speed of further rate rises and how that's going to play out."
Meanwhile, a Commerce Department report showed weaker-than-expected US consumer spending, increasing 0.2 per cent in May, after being steady in April.
But analysts, like Bullard, point to more recent signs that justify optimism about the outlook.
"We have evidence of consumer spending continuing at a very good pace in June. That limits my concerns," Anthony Karydakis, chief economic strategist at Miller Tabak in New York, told Reuters.
In a separate report, the Labor Department said new applications for state unemployment benefits fell 2,000 to a seasonally adjusted 312,000 for the week ended June 21.
In the final hour of trading in New York, the Dow Jones Industrial Average fell 0.12 per cent, the Standard & Poor's 500 Index declined 0.16 per cent, while the Nasdaq Composite Index dropped 0.1 per cent.
Declines in shares of Wal-Mart, last down 1 per cent, and those of Microsoft, last down 0.9 per cent, led the slide in the Dow.
Shares Bed Bath & Beyond sank, last down 7.3 per cent, after the company offered an outlook that fell short of expectations.
In Europe, the Stoxx 600 Index finished the session marginally lower from the previous close at 341.86. CAC 40 fell 0.5 per cent, while Germany's DAX declined 0.6 per cent. The UK's FTSE 100 eked out a gain of just under 0.1 per cent.