Senate Finance Chairman Max Baucus (D-Mont.) said on Thursday that the provision should be scuttled for now and instead put on his committee's agenda for a markup as part of a broader tax reform package.
"There are going to be a ton of amendments that are not going to be appreciated by the supporters of this bill, and they are going to dramatically weaken what they think they might have," he said.
Baucus suggested that more time be taken to consider the unintended consequences of the bill.
"I think this amendment is not yet ready. It's premature," he said.
Montana is one of five states without a sales tax.
Groups such as the National Retail Federation (NRF) and the Retail Industry Leaders Association (RILA) have put their weight behind the measure, while firms such as eBay oppose the provision, calling for better protections for small businesses.
The measure exempts small businesses that earn less than $1 million annually from out-of-state sales.
Retailers and lawmakers argue that states are hampered by a 1992 Supreme Court decision that says companies only have to collect sales taxes from consumers in states where they have a physical location. State tax laws require consumers to declare unpaid sales tax, but few do.
During debate on Thursday, Durbin argued that the bill would help brick-and-mortar business better compete in the online age where many retailers don't collect sales taxes.
Alexander argued the bill is an issue of "states rights" and without the ability to collect the taxes, many states may need to increase other taxes to make up for lost revenue, especially as state and local governments continue struggling to keep their coffers filled enough to handle basic services.
Two of the amendment's co-sponsors are Democratic Sens. Mark Pryor (Ark.) and Heidi Heitkamp (N.D.) who have yet to decide whether they will back their party's plan.
The amendment was met with resistance on the Senate floor Thursday.
But the co-sponsors argued that they been pushing the legislation for the better part of two years and now is the time to move forward.