The bill would also create an English language requirement for naturalization into the United States, and require the federal government to encourage people to learn the language.

"We must make assimilation of our legal immigrants a top priority and learning English is an important first step in that process," King said this week. "The English Language Unity Act is bipartisan legislation that will enshrine English as the official language of our nation, and ensure that this powerful force binds us all together so that all have the ability to achieve the American dream."

While the bill is largely backed by Republicans in the House, it does boast a few Democratic cosponsors: Reps. Mike McIntyre (N.C.) and Nick RahallNick Joe RahallWe shouldn't allow politics to impede disaster relief Break the cycle of partisanship with infant, child health care programs Clinton mulls role in 2018 midterms MORE (W.Va.).

Inhofe said this week that as Congress considers immigration reform, the English-only bill should be part of that discussion.

"Congress will likely be debating comprehensive immigration reform this summer, and any reform to our immigration laws must include English language provisions," he said. "We are a nation built by immigrants, and it is important we share one vision and one official language."

In the last Congress, King's bill ended up with 122 cosponsors. But while it was the subject of a House Judiciary subcommittee hearing, it was not brought to the floor for a vote in the Republican-led House.

The bill is H.R. 997 in the House and S. 464 in the Senate.