RLHF-style alignment trains language models to refuse unsafe requests, but how much operational margin does this refusal rest on? We introduce the refusal-affirmation logit gap: the difference between the top refusal-token logit and the top affirmative-token logit at the first decoding step. This single scalar quantifies the per-prompt safety margin that alignment provides. Empirically, alignment widens the gap on 97.5-99.8% of toxic prompts across three model families, and median gap closure co-varies with True-ASR ranking across suffix strategies (an internal consistency check, since our method optimises gap closure). To validate the metric's practical significance, we present logit-gap steering, a gradient-free, forward-pass-only method that discovers short in-distribution suffixes ($<$10 tokens per component) whose cumulative effect closes the gap. The method requires ${\approx}26{,}000$ forward-pass equivalents per family (${\approx}2$~min on one A100), ${\approx}125\times$ less than a single GCG search. Suffixes discovered on 0.5B--2B models transfer without modification to 72B within family. An 8-suffix ensemble reaches 38-96\% True ASR across 13 models on AdvBench and HarmBench, with most suffixes having $10^{3}$-$10^{4}\times$ lower perplexity than GCG-meaning published perplexity-filter defenses that collapse GCG (64.7%$\to$1.0%) leave our suffixes nearly intact (76.9%$\to$76.0%). These results demonstrate that current alignment margins, while consistently present, can be thin and efficiently measurable, and that defense strategies must account for in-distribution suffixes.