For Senator Roy Blunt of Missouri, it is a bridal shop in St. Louis where customers try on dresses, check the labels for the product code, and then order the same product online, free of sales tax.

For Representative Austin Scott, an ardent conservative Republican from Georgia, it’s Ken’s Trading Company, where the profit margin on a Leupold rifle scope is lower than the sales tax too many Georgians are avoiding by shopping for the same scope on their computers.

“We respect their opinion. I’m glad they’re there as conservatives,” Mr. Scott said of the antitax groups. “But the fact of matter is, in the end we have a job to do.”

For opponents of the bill, the impotence of the antitax arguments has been a revelation.

“I don’t think any one group drives an issue. It’s the issue itself,” said Senator Kelly Ayotte, Republican of New Hampshire, whose state is one of five with no sales taxes. “What does surprise me, put aside the groups for a minute, is that there are people who describe themselves as conservatives who are going to support this act, when regardless of how you look at it, whether your state has a sales tax or not, it’s going to put some fairly rigorous and onerous requirements on online businesses to collect taxes for other states. That’s counter to conservative principles.”

The Internet sales tax is not the first battle such groups have lost, but it might be one of the clearest. In 2010, just before all of the Bush-era tax cuts were first set to expire, President Obama and Senate Republican negotiators reached agreement to extend all of the tax cuts for two years, except one.

The estate tax had actually expired. Rather than have it reborn at the relatively high top rate of Bill Clinton’s era, negotiators allowed it to come back at a considerably lower rate. It was still a tax increase from zero, but not as big as it could have been. Mr. Norquist blessed it.

He took his argument even further this year when all those tax cuts expired again. This time, Mr. Obama insisted that tax rates rise considerably on upper-income families’ wages, estates, capital gains and dividends. Almost all Republicans saw that as a tax increase, and a big one, but Mr. Norquist — seeing that passage was inevitable — again declared that the deal did not violate his group’s no-new-taxes pledge since letting all the tax cuts expire would be worse.