A Republican proposal that would tax retailers on goods they import and sell in the U.S. still has more questions than answers.

But that hasn't stopped industry leaders and trade groups from increasing the pressure they're putting on Washington, D.C., as they fight against a policy critics say could put some of these companies out of business.

A "large number of CEOs" have been to D.C. in recent months, to share their concerns about a so-called border adjustment tax, David French, senior vice president for government relations at the National Retail Federation, told CNBC.

When factoring in visits from CFOs, those numbers are "easily" in the double digits, French said.

Separately, the Retail Industry Leaders Association (RILA) on Wednesday formally launched a national campaign to fight the border tax, called Americans for Affordable Products.

A vice president for that trade group recently told Jefferies that participants across the industry have reached out about the issue, "including retailers who typically do not engage in public policy issues," Jefferies analyst Randal Konik said.

RILA's members include major retailers like Target, Home Depot, J.C. Penney, Wal-Mart and Nike. Of those retailers, only Target and Home Depot responded to CNBC's request for comment. A Home Depot spokesman said the company is "still studying the possible scenarios and impacts."

A Target spokeswoman echoed that statement, saying the retailer is "closely monitoring the ongoing discussions on tax reform and the impact of the House's proposed border adjustability tax on our guests." The spokeswoman confirmed to CNBC that Target CEO Brian Cornell was one of the industry executives who went to Washington to speak out about the tax, as was first reported by Politico.

"We can confirm that [CEO Brian Cornell] traveled to D.C. to participate in conversations with lawmakers but we are not going to get into specifics of those conversations," Target spokeswoman Dustee Tucker Jenkins said.



However, a source close to the matter told CNBC that Target's message is centered on the impact a border tax would have on its shoppers, who would end up paying more for the company's products. The retailer is also emphasizing the fact that 99 percent of its workforce is based in the U.S., and that a border tax would slow its plans to open small, urban stores that would employ more Americans.

"In the last decade, no issue has galvanized the industry more than this one," Brian Dodge, senior executive vice president of public affairs at RILA, told CNBC.