This is a study of the safety, tolerability, pharmacokinetics (PK), and pharmacodynamics (PD) of MK-8666 in participants with type 2 diabetes mellitus (T2DM). Participants enrolled in this trial would be either treatment-naive or have washed off of oral anti-hyperglycemic agents. MK-8666 is planned to be administered orally for up to 2 weeks. The primary hypothesis for this study is that after 14 days of once daily treatment with MK-8666, at a dose that is safe and well tolerated, the placebo-corrected fasting plasma glucose reduction from baseline is ≥34 mg/dL.