Brown, whose own proposal to eliminate the withholding rule did not clear a procedural vote last month, introduced repeal legislation on Monday that passed the House last week.
Under the House plan, a proposal to toughen eligibility requirements for Medicaid would be used to offset the 3 percent repeal.
The House passed the two measures separately last week, with the Medicaid proposal proving much more controversial. While only 16 Democrats voted against 3 percent repeal, the vast majority of the caucus — 157, in all — opposed the health bill.
For his part, Brown had previously called for making up for the lost revenue by rescinding unused discretionary funds.
But Democrats balked at that idea; Senate Majority Leader Harry Reid (D-Nev.) said last month that he would prefer to use a tax break for corporate jet owners and other revenue-raisers to pay for repeal. Reid has also said he wants further assurances that contractors are compliant on their taxes.
On Tuesday, the Chamber’s Giovanni Coratolo and small-business owners joined Brown to call on the Senate to push repeal “across the finish line.”
Coratolo, the Chamber’s vice president for small business policy, said that the 3 percent rule, if allowed to go live, could lead to making infrastructure improvements more costly and make life more challenging for doctors and other healthcare professionals.
Brown, meanwhile, said he hoped that taking aim at the 3 percent rule would be just one of several areas included in President Obama’s $447 billion jobs package where the two parties could find common ground.
Before the White House backed the House repeal measure, it had proposed delaying the 3 percent rule another year, to 2014.
The Senate has already blocked the president’s entire jobs package and a plank from the broader measure that would create or save police, firefighting and teaching jobs. Democrats proposed paying for both those bills with a surtax on millionaires.
Senate Democrats are currently pushing an infrastructure portion of the jobs bill. But Brown signaled Tuesday that there were other parts of the president’s plan that could get more bipartisan support, such as incentives for hiring veterans.
“We should get those things out the door right now,” Brown said.