It would. It also has a zero chance of making it through a Democrat controlled Congress. However, legislation like this should be submitted regularly rather than allow the issue to die.
I'm thinking that even though this is a federal issue, the states' legislatures are going to have to be the place where the legislation is passed, since the eligibility ought to be established in order to be placed on each state's ballot. As I wrote earlier, it should not be confined to establishing a presidential candidate meets the natural-born requirement, every person standing for election to the House and Senate must be citizens first, residents of the district/state in which they wish to represent, this also should be a part of the qualifier-legislation, seeing as how a person who isn't even a citizen was allowed onto a state's ballot. Who knows how many non-citizens have attempted to run for a House or Senate seat, but lost the election?
Democrats can be persuaded to vote against the party interest, if they’re interested in keeping their floozie little jobs. Heath Shuler in NC is a prime example of this. Kissell, the complete neophyte who nearly defeated Hayes in the same election cycle, and did defeat him this go ‘round, is another. The wave of “populist” disgust that so many so-called “blue dog” Democrats rode to office in the past two years makes them vulnerable.