A two-page ballot caused havoc for scanning machines at polling places across New York City, as scores of broken scanners brought voting to a standstill at many locations on an Election Day marked by heavy turnout.

Imagine that feeling of an office copier jammed with paper just as you’re trying to fetch an important document. Now multiply that feeling by 100. That’s about how people felt as they waited in lines that circled around school gyms and around the block at their local polling places. Voters waited helplessly as the scanners stood idle.

Mayor Bill de Blasio called the situation at poll sites “absolutely unacceptable” and said it showed that the city’s Board of Elections was “broken.” On Tuesday afternoon, he told 1010 WINS radio that the State Legislature must pass a law to turn the board into “a modern agency that knows how to provide the services it’s charged with.”

The City Council speaker, Corey Johnson, went a step further on Twitter, calling for the resignation of the executive director of the city’s Board of Elections, Michael J. Ryan, after Mr. Ryan told reporters that the damp weather was moistening ballots and contributing to the scanner problems.