The Senate is hurtling toward a critical window to advance a landmark proposal to regulate cryptocurrency, but negotiators face a steep climb as some Democrats dig in over concerns the bill does too little to curtail ethics breaches and illicit finance.

Top Republicans have called for the chamber to take up the Digital Asset Market Clarity Act (H.R. 3633), known as the CLARITY Act, once senators return July 13 and before lawmakers retreat for August recess — after which congressional activity typically slows in election years. A White House official said they’re working to make sure the bill …