In 2018, Swiss citizens voted for fostering cycling to be included in the Swiss Constitution. This national vote and a post-vote survey among a representative sample of citizens bring insight into the varying propensity to support cycling among the population. The main explanatory factor is participants’ current cycling practices: cyclists were much more likely to vote positively, as they are more aware of the lack of infrastructure. Non-cyclists were more reluctant, perhaps because they do not wish to challenge the dominant system of automobility. The second most important factor is a right–left political gradient. People on the left were more likely to vote positively and to agree with the arguments for the inclusion of cycling in the Constitution (safety, reduction of congestion, environmental and health benefits), while people on the right were more likely to agree with counterarguments (cycling network already excellent, federalism, unfair to foster cycling). Support for the vote did not vary significantly between social classes, ages or residential contexts. Women, who cycle less than men, voted more in favor and were more concerned about safety, which may be interpreted as a latent demand to cycle. A desire to “catch up” was also observed on the regional level: cantons with a low modal share of cycling were characterized by a higher acceptance rate.