The Wisconsin Republican said on Sunday that attacks inspired by IS, like the one against the provocative cartoon contest in Texas a week ago, are allowing the group to convey a "winner's message", CNN reported.
Johnson chairs the Senate Homeland Security and Governmental Affairs Committee.
"The best strategy the US can employ to defeat this is actually defeat IS in Iraq and Syria so that the reality is conveyed that this is not a winning organisation, it is a losing organisation," he said.
Johnson admitted, though, that tracking IS sympathisers in the US is a particular challenge, since the group has communicated with potential recruits over social media and law enforcement officers cannot track every possible suspect.
"The problem is, what do you do with the not-guilty-yet?" Johnson said.
He cited a figure published in March: There are about 46,000 -- though maybe as many as 90,000 -- Twitter accounts that support IS.
"... just consider maybe 90,000 people drawn to this barbaric ideology. So we have got a very large haystack. We're looking for a needle in it."
Brett McGurk, the US envoy for the Global Coalition to Counter IS, said 22,000 foreigners have joined the terror group's ranks in Iraq and Syria.
Of those, McGurk said, 3,700 are from Western nations. One eighty Americans have sought to join the organisation, 15 of those have been charged with supporting IS by the justice department.
Other experts said the threat of IS now is greater than what Al Qaeda posed to the US at the time of the 9/11 attack.
"Remember back then we thought about Al Qaeda in Afghanistan and Pakistan and a few other places?" said Tom Ridge, who served as secretary of Homeland Security under President George W. Bush.
"Well, we've seen Al Qaeda metastasize. It is now a global scourge. And you have the ascendancy of IS. The combination of those two groups -- their appeal to the lone wolfs and we see them acting in Belgium and in France and in Canada and the US."