The bill would eliminate the requirement that businesses must file the forms to the IRS for every vendor with whom they have at least $600 in transactions.
Senate Democratic leaders are expecting to pass the Federal Aviation Administration measure this week.
The two-year $34.5 billion measure to reauthorize the FAA includes $8 billion for airport construction.
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Johanns failed twice last year to push through a bill even Democrats, Republicans and the White House agreed that the provisions would place an "onerous burden" on businesses.
He credited President Obama's backing of the repeal combined with lawmakers learning about this issue for his bill's fast popularity in the 112th Congress.
In the past, the battle has ensued over how to pay for the measure and cover about $19 billion in estimated lost revenue.
The Johanns bill authorizes the Office of Management and Budget to identify unobligated federal funds to cover the cost of repeal.
Senate Finance Chairman Max BaucusMax Sieben BaucusBiden nominates Nicholas Burns as ambassador to China Cryptocurrency industry lobbies Washington for 'regulatory clarity' Bottom line MORE (D-Mont.) and Senate Majority Leader Harry ReidHarry Mason ReidHarry Reid calls on Democrats to plow forward on immigration Democrats brace for tough election year in Nevada The Memo: Biden's horizon is clouded by doubt MORE (D-Nev.) have also introduced a similar measure this week.