Recent research suggests that Vision Language Models (VLMs) often rely on inherent biases learned during training when responding to queries about visual properties of images. These biases are exacerbated when VLMs are asked highly specific questions that require selective visual attention, a demand that mirrors cognitive challenges observed in human enumeration tasks. We build upon this research by developing a synthetic benchmark dataset and evaluation framework to systematically characterize how counting performance varies as image and prompt properties change. Using open-source VLMs, we analyze how performance shifts across controlled perturbations (e.g. number of objects, object color, background color, object texture, background texture, and prompt specificity) and examine corresponding changes in visual attention allocation. We further conduct exploratory attention reweighting experiments in the language model decoder to modulate focus on visual tokens at different layers and assess their effects on counting behavior. Our results reveal that counting accuracy degrades systematically with increasing visual and linguistic complexity echoing human limits and cognitive load effects known from human perception, while targeted attention reweighting yields modest but measurable improvements. Rather than competing on benchmark accuracy, we introduce a controlled diagnostic framework for analyzing VLM enumeration behavior. Through systematic experiments, we expose failure modes rooted in cross-modal binding that natural image benchmarks may not easily isolate, and provide preliminary empirical evidence that targeted attention reweighting in the language decoder can influence how models ground linguistic quantity concepts in visual representations. Code and data available here: https://github.com/ssen7/vlm-count-analysis