Nearly every minor party has fallen short of collecting 250,000 votes, including, and perhaps especially, the Working Families Party, a progressive group that shares many Democratic Party ideals yet has been one of the most reliable antagonists of Mr. Jacobs and his close ally Mr. Cuomo.

Only the Conservative Party has been able to surpass the 250,000 vote mark in recent years. If just that party survived, a candidate could then run on both the Conservative and Republican lines — New York election law allows candidates to run on multiple lines — while a liberal candidate would have no such advantage.

“Conservatives have an awful lot of support,” Mr. Jacobs said when asked about the idea. “There’s no question that they will have an easier time meeting these thresholds.”

“I can see that that could be problematic,” he added.

Mr. Jacobs, whom Mr. Cuomo appointed to the state commission, insisted that his proposal was aimed at reducing voter confusion and rooting out corruption among “sham” parties that he said trade their ballot lines for political favors. He did not specify which parties he was referring to.

“A lot of people have been getting away with an awful lot for a long time,” Mr. Jacobs said. “In my mind, it will be better overall if elections are run with only really credible parties.”