"More importantly, we are really thinking about a path, we are talking about moving interest rates from zero to a normal level over several years," he said, echoing recent comments by several other Fed policymakers.
"So even if the economy got some bad shocks, really you are probably just talking about flattening that path out a bit, or maybe raising rates more slowly."
Lift-off, data and T-shirts
To get that message across Williams has begun giving away T-shirts, printed at his own expense, showing an arrow busting upwards out of a computer and declaring: "Monetary policy—It's data dependent."
The slogan captures a shift increasingly evident in the language of some of the Fed's most influential policymakers - away from concerns about acting "too early" toward a focus on calibrating rates in a way that will sustain steady recovery.
Read MoreSummers to Fed: Pre-emptive inflation war is dangerous
In fact, the Fed now needs to weigh the risks of waiting too long before a rate lift-off, Williams said. The concern is a late start to rate increases could force the Fed to tighten policy more aggressively and potentially disruptively if stronger economic growth sparks inflation pressures.
"A little earlier and more gradual versus later and more aggressive: those are the options we have," Williams said.
To be sure, some policymakers, notably the presidents of the Minneapolis and Chicago Fed banks, still argue that raising rates too soon poses a bigger risk than waiting too long.
Economists last month pushed their expectations of a rate hike later into 2015 from mid-year after the Fed downgraded its economic outlook. However, recent policymaker comments suggest the Fed would be still poised to act if data over the next two months confirmed continued job growth and an expected rebound from the weak start to the year.
In the last two weeks, three Fed governors have laid out the argument that it is the longer rate path, not the date of lift-off, that matters. Jerome Powell in New York last week made the direct case that the Fed should not wait to act until its goals of full employment and 2-percent inflation are in view.