WASHINGTON — A bipartisan Senate bill that would overhaul the rules governing college athletics is facing growing opposition, putting its future in doubt even as its chief sponsors say they are close to a vote. Senate Commerce Committee Chair Ted Cruz, a Texas Republican, and ranking member Maria Cantwell, a Washington Democrat, said Monday that lawmakers were “on the cusp” of advancing the legislation. Cruz compared the negotiations to reaching the one-yard line and said supporters hoped to hold an initial floor vote as soon as this week, though he acknowledged it could slip to next week. The bill would create a broad federal framework for college sports, an area now shaped by a patchwork of state laws, NCAA rules and court decisions. Its passage could represent one of Congress’ most consequential actions on college athletics before the midterm elections. But Senate Majority Leader John Thune offered a more cautious assessment. Asked whether supporters had the 60 votes needed to advance the measure, Thune said, “We’ll see if we have 60 — I don’t know the answer for sure on that yet.” The legislation has faced resistance from several directions. Wisconsin Republican Sen. Ron Johnson said he was not a supporter of the bill and described it as “way too prescriptive.” Johnson also questioned whether the federal government should play such a significant role in regulating college sports. Some Republicans had been concerned that the bill could override state laws governing whether transgender athletes may participate on women’s sports teams. Cruz said negotiators addressed those concerns by adding language to the legislation. The changes, however, have not resolved all Republican objections. Labor and civil rights organizations also mobilized against the bill Monday. The Service Employees International Union and allied groups urged senators to oppose it, while Democratic Sen. Chris Murphy of Connecticut appeared with the AFL-CIO to criticize the measure. Murphy said opponents would do everything they could to persuade senators not to move forward, arguing that the current proposal would preserve an exploitative system that harms athletes. The criticism reflects broader concerns about whether college athletes would receive adequate protections and bargaining power under a national system shaped largely by universities, conferences and the commercial sports industry. At least one Senate Democratic aide familiar with private negotiations said the coalition opposing the bill was expanding, despite the optimism Cruz and Cantwell displayed publicly. The aide was granted anonymity to discuss the closed-door talks. The bill’s supporters have been negotiating changes intended to secure bipartisan backing. Their challenge is to balance competing demands from universities and athletic conferences, athletes and labor advocates, state lawmakers, and senators who oppose a larger federal role. For college athletes and their families, the debate could determine whether rules on compensation, eligibility, athlete protections and state authority become more uniform nationwide. A federal system could reduce uncertainty for schools and athletes operating across state lines, but opponents say a sweeping law could lock in the influence of powerful athletic organizations without giving athletes a meaningful role in setting the rules. Cruz and Cantwell have not set a final vote date. With the Senate’s legislative calendar tightening ahead of the elections, a delay could make it harder to complete the negotiations and pass the bill this year.