Recently, researchers claimed that people are intuitively inclined to cooperate with reflection causing them to behave selfishly. Empirical support for this claim came from experiments using a 4-player public goods game with a marginal return of 0.5 showing that people contributed more money to a common project when they had to decide quickly (i.e., a decision based on intuition) than when they were instructed to reflect and decide slowly. This intuitive-cooperation effect is of high scientific and practical importance because it argues against a central assumption of traditional economic and evolutionary models. The first experiment of present study was set up to examine the generality of the intuitive-cooperation effect and to further validate the experimental task producing the effect. In Experiment 1, we investigated Amazon Mechanical Turk (AMT) workers' contributions to a 4-player public goods game with a marginal return of 0.5 while we manipulated the knowledge about the other players' contribution to the public goods game (contribution known vs. contribution unknown), the identity of the other players (humans vs. computers randomly generating contributions) and the time constraint (time pressure/intuition vs. forced delay/reflection). However, the results of Experiment 1 failed to reveal an intuitive-cooperation effect. Furthermore, four subsequent direct replications attempts with AMT workers (Experiments 2a, 2b, 2c and Experiment 3, which was conducted with naïve/inexperienced participants) also failed to demonstrate intuitive-cooperation effects. Taken together, the results of the present study could not corroborate the idea that people are intuitively cooperative, hence suggesting that the theoretical relationship between intuition and cooperation should be further scrutinized.