Construction grammar posits that constructions, or form-meaning pairings, are acquired through experience with language (the distributional learning hypothesis). But how much information about constructions does this distribution actually contain? Corpus-based analyses provide some answers, but text alone cannot answer counterfactual questions about what caused a particular word to occur. For that, we need computable models of the distribution over strings---namely, pretrained language models (PLMs). Here we treat a RoBERTa model as a proxy for this distribution and hypothesize that constructions will be revealed within it as patterns of statistical affinity. We support this hypothesis experimentally: many constructions are robustly distinguished, including (i) hard cases where semantically distinct constructions are superficially similar, as well as (ii) schematic constructions, whose slots'' can be filled by abstract word classes. Despite this success, we also provide qualitative evidence that statistical affinity alone may be insufficient to identify all constructions from text. Thus, statistical affinity is likely an important, but partial, signal available to learners.