This is far from the first time such a proposal has surfaced. In 2008, U.S. Rep. Zoe Lofgren, (D-Calif.), and Rep. Bob Goodlatte, (R-Va.), co-sponsored a similar bill. But Smith is chairman of the House Judiciary Committee, which has oversight over immigration. That puts this bill in a good position to advance.

Lofgren has been leading an effort to get a that would affect green cards and H-1B visas, but Republicans have shown no signs of backing that proposal.

Chaffetz, in a statement, said that the legislation is supported by a coalition of high-tech companies that includes Microsoft, Google and Oracle.

Michael Wildes, a managing partner at Wildes & Weinberg PC, an immigration law firm, said there are multiple ways for people to qualify for status. As a result, the proposal to eliminate the per-country cap "really doesn't have a significant effect."

On the Facebook town hall will be Rep. Eric Cantor, (R-Va), the House majority leader; Kevin McCarthy, (R-Calif.), the majority whip; and Paul Ryan, (R-Wisc.), the House budget committee chairman. Joining them will be Sheryl Sandberg, the COO of Facebook.