Congressional Republicans, Democrats and the White House have called the provision "burdensome." Although a repeal of the provision has bipartisan support, lawmakers couldn't reach an agreement last year.
"We've never had this much support, so I'm very encouraged," Johanns said.
Senate Finance Chairman Max Baucus (D-Mont.) also plans to introduce a measure.
Both parties have seized on the 1099 requirement to score political points. Republicans are posing repeal of 1099 as part of their promise to chip away at the reform law, while Democrats are touting it as a sign of their willingness to improve the current law.
Jason Millman contributed to this article.
This article was updated at 1:40 p.m.