As all realistic citizens recognize, cops aren’t just thugs-with-badges. They are liars, too.
While a cop may imply that failure to speak immediately will result in arrest, a person cannot be arrested for exercising the right to remain silent. Police can only arrest a person if probable cause exists, and the choice to remain silent cannot be part of that analysis. If the officers already have probable cause, they would not need to question you. If they do not, the statement you make could well supply it.