Context. The rotational properties of small near-Earth asteroids (NEAs) provide crucial insights into their internal structure and collisional history. However, systematic surveys targeting metre- to decametre-sized bodies are rare, thus leaving their spin distribution poorly constrained. Aims. Our aim was to quantify the prevalence of fast rotation and characterise the spin-rate distribution of small NEAs to constrain their internal strength and evolution. Methods. We conducted a dedicated high-cadence photometric survey of 249 NEAs using the Two-meter Twin Telescope (TTT). Rotation periods and amplitudes were derived from dense time series to classify objects as fast or non-fast rotators. Results. We determined the rotation period of 156 new fast rotators (P < 2.2 h), including 87 that rotate faster than 10 min. The prevalence of fast rotators increases with absolute magnitude: from 60.6─80.3% for 22 < H < 24 to 77.3─89.4% for 24 < H < 26 and 94.1─96.1% for H > 26, indicating that fast rotation dominates in the small NEA population. Most objects spin faster than the gravity-defined limit; 98 targets require cohesive strengths exceeding that of weak rubble piles, and 22 are compatible only with compact, high-strength interiors. Conclusions. This is the first systematic survey targeting the rotation of such small NEAs, providing the largest homogeneous sample of fast rotators obtained by a single campaign. Our findings demonstrate that fast rotation is the norm for objects smaller than tens of metres, implying that modest cohesive strength is required to prevent their rotational disruption.