The Temporary Duty Suspension Process Act is backed by Senate Minority Leader Mitch McConnellAddison (Mitch) Mitchell McConnellSessions: 'We should be like Canada' in how we take in immigrants NSA spying program overcomes key Senate hurdle Overnight Finance: Lawmakers see shutdown odds rising | Trump calls for looser rules for bank loans | Consumer bureau moves to revise payday lending rule | Trump warns China on trade deficit MORE (R-Ky.) and Minority Whip Jon Kyl (R-Ariz.), as well as other key Republicans. Portman, McCaskill's partner in developing the bill, is a former U.S. Trade Representative under President George W. Bush.

"It's gratifying to see that bipartisan compromise is possible in Congress — especially on an issue as important as boosting American jobs and helping our manufacturers," McCaskill said.

Tariff reductions on inputs that are generally not made in the United States are seen as a boost for U.S. companies, as the reductions lower import costs and help companies compete overseas. But for several years, companies have had to secure these tariff breaks by asking their members of Congress to file legislation.

House Republicans balked at that process at the start of the 112th Congress, as they saw these bills as earmarks, which they had vowed to avoid.

While many of those members are coming around to the idea that the bills grant a tax break, and are not earmarks, the McCaskill bill would circumvent the debate by changing the process for building a so-called Miscellaneous Tariff Bill (MTB). Under her bill, companies could file requests for tariff reduction through the International Trade Commission (ITC).

The bill would also allow members of Congress to recommend a tariff reduction, or do so through a petition from an outside party. The ITC would recommend tariff suspensions to Congress after assessing such requests.

"These changes would bolster accountability by lessening the chance for backdoor earmarks, and would improve the process for job-creators, as they would no longer be forced to hire high-paid lobbyists to help get individual legislation introduced at the start of the process," McCaskill's office explained.