(The Hill) — The Senate is plowing forward with consideration of the Social Security Fairness Act, clearing its first procedural hurdle on what supporters hope is a path to passage later this week. The Senate voted 73-27 to advance the measure, which could mean higher Social Security benefits for some Americans if passed before Congress leaves this week. The bill would repeal the Windfall Elimination Provision and the Government Pension Offset. Supporters say the overhaul of the tax rules is key to preventing unfair reductions in benefits for millions of people who have worked in public service. But experts have sounded alarm over the measure, saying the rules it targets are aimed at preventing some beneficiaries from collecting both their pensions and relatively higher Social Security payouts than earned. The bill, which passed with widespread support in the House, has backers lining up on both sides of the aisle. That includes Sen. Mike Braun (R-Ind.), a prominent conservative and deficit hawk who was recently elected the next governor of Indiana. Asked about the bill’s projected price tag, Braun told The Hill on Wednesday that he is "going to vote for it, simply because it's an inequity.” “Normally, if it didn't have a pay for, I wouldn't vote for anything I like the policy on. I've only done that where I felt it's been an inequity that underlies it in the first place,” he said. Making the case for the bill on Wednesday, Senate Majority Leader Chuck Schumer (D-N.Y.) said it would “ensure no American who has chipped into Social Security is wrongly denied their well-earned benefits.” How to claim a 2nd payment from the Equifax data breach settlement “This afternoon, we will vote whether or not to take up the Social Security Fairness Act, a bill repealing two flawed policies that eat away at the benefits of many Americans who at some point or another worked as teachers, firefighters, postal workers, or other public sector workers.” Some Republicans have expressed concerns about what it could mean for the program’s insolvency date. “I think it's very disrespectful to the people who are on Social Security to expand Social Security when Social Security is already in the process of going bankrupt,” Sen. Rand Paul (R-Ky.) told The Hill on Wednesday. “I don’t think conservatives are supporting this bill.” The Congressional Budget Office estimated the bill would cost upward of $190 billion over a decade. It also projected in a letter last month that Social Security’s trusts funds could “be exhausted roughly half a year earlier than it would be under current law” if the bill were enacted.