The Federal Reserve's decision to cut its key borrowing rate by a quarter percentage point seems to be sitting well with the White House, if National Economic Council Director Kevin Hassett is any indication.

In a CNBC interview Thursday, the day after the Fed's move, Hassett noted that the administration, and new Fed Governor Stephen Miran, had been pushing for a bigger reduction. Miran, who is on leave as head of the Council of Economic Advisers, pushed for a half-point cut but was outvoted 11 to 1 on the Federal Open Market Committee.

However, Hassett was not critical of the committee's decision.

"The bottom line is that moving kind of slow and steady and heading towards a target, watch the data come in, that's what prudent policy is," he said on " Squawk Box ." "So I know that m

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