WASHINGTON—Sen. Bernie Sanders, whose liberal call to action has propelled his long-shot presidential campaign, is proposing an array of new programs that would amount to the largest peacetime expansion of government in modern American history.

In all, he backs at least $18 trillion in new spending over a decade, according to a tally by The Wall Street Journal, a sum that alarms conservatives and gives even many Democrats pause. Mr. Sanders sees the money as going to essential government services at a time of increasing strain...