The days of tax-free shopping at Amazon could be coming to an end — at least if merchants in Massachusetts and other states have their way.

Local retailers are heading to Beacon Hill tomorrow as part of a new fight to force e-commerce sites like Amazon, Overstock, and Zappos to collect sales tax from local residents.

The Retailers Association of Massachusetts for the first time is pushing a bill that aims to level the playing field with online behemoths who they say have an unfair advantage because they do not charge sales tax. With the backing of chains like Wal-Mart and Best Buy, the group is also launching a coalition to support the cause.

“If we have to collect sales tax, then so should our competitors on the Web,’’ said Jon Hurst, president of the retailers group, which is organizing the Massachusetts Main Street Fairness Coalition.

The pressure in Massachusetts comes as other states escalate efforts to collect sales tax from large online retailers. Similar bills have passed in New York, Rhode Island, and Illinois, and another dozen states are considering legislation. According to the National Conference of State Legislatures, states missed out on an estimated $8.6 billion in 2010 from failing to collect sales tax for online and catalog purchases. In the Commonwealth, the sales tax loss is projected at $335 million for 2012.

Erik Brynjolfsson, director of the MIT Center for Digital Business, said as a growing number of states pass these laws, it will become more difficult for Amazon and other e-commerce businesses to avoid the issue.

“There was a time when the Internet was a very small share of retail commerce and maybe it wasn’t worth pursuing, but now in a lot of categories, e-commerce is larger than offline retailers,’’ said Brynjolfsson, an MIT Sloan School of Management professor.

Representative Martin J. Walsh, a Dorchester Democrat who sponsored the bill, said it is too early to gauge support, but he hopes to see it advance within the year. “This is less about collecting taxes and more about a question of fairness,’’ he said. “This levels the playing field for retailers in Massachusetts who are losing sales to the Internet.’’

E-commerce businesses have been protected by a 1992 Supreme Court ruling that mandated retailers to collect sales tax only in states where they have a physical presence. The proposed bill in Massachusetts — scheduled for a hearing tomorrow before the Joint Committee on Revenue — expands the definition of physical presence to include what are known as affiliates.