The Republicans who are going to be in charge of matters related to immigration, Rep. Steve King of Iowa and Rep. Lamar Smith of Texas, have some pretty radical ideas on immigration. So you can expect to see a lot of this over the next two years (via Steve Benen):
GOP Rep. Steve King of Iowa, the incoming chairman of the subcommittee that oversees immigration, is expected to push a bill that would deny "birthright citizenship" to such children.
The measure, assailed by critics as unconstitutional, is an indication of how the new majority intends to flex its muscles on the volatile issue of illegal immigration.
Such a proposal isn't going to become law, and even if it did, it would be plainly unconstitutional under the 14th Amendment. You'd need to amend the Constitution in order to eliminate birthright citizenship, and that's not going to happen. The interpretation of the 14th Amendment that King is depending on here to support the idea that children born to undocumented immigrants on American soil aren't actually citizens is laughably dumb. Then there's the fact that the most immediate effect of repealing birthright citizenship would be an increase in undocumented immigrants. Depending on how it's done, repealing birthright citizenship would increase the population of undocumented immigrants from 11 million today to between 16 million and 24 million by 2050.
But if your goal is reducing the number of Latino citizens, rather than stopping illegal immigration, then the policy makes sense. It's still an unconstitutional symbolic gesture that won't do any good, but it's the kind of culture-war-driven governance that the conservative base is looking for.