New York (CNN) - Four days after a monster blizzard blanketed much of the northeastern U.S., New York Mayor Michael Bloomberg said he will investigate whether sanitation workers intentionally delayed cleanup efforts over frustrations regarding citywide budget cuts.

"It would be an outrage if it took place," Bloomberg said Thursday, stressing that his administration's primary focus is clearing streets in the city's outer boroughs. Some neighborhoods remained snowbound for days after the storm.

Rumors swirled across New York on Thursday that sanitation officers ordered rank-and-file workers to slow down cleanup efforts in retaliation for the city's belt-tightening measures.

City councilman Dan Halloran said three sanitation workers and two Department of Transportation supervisors came to his office saying their supervisors ordered the slowdown, telling workers "The mayor will see how much he needs us" and that "there will be plenty of overtime."

Councilman Halloran addresses how large the problem was on American Morning.