Loretta Sanchez eked out an election win in 1996 by less than 1,000 votes. After a recount that determined her margin of victory was 984 votes, Sanchez was seated in the House, but Dornan (her opponent) protested, alleging illegal votes cast. In 1998, the House Oversight Committee dismissed Dornan's challenge after concluding that 750 to 800 votes cast were invalid, still short of Sanchez's 984-win, based on crosschecks with immigration records. House Speaker Newt Gingrich (R-Ga.) said if the number of illegal votes matched Sanchez's winning margin, action would have been taken. A resolution was passed in the House later that month dismissing the challenge.H. Res. 355, Feb. 12, 1998(10)H. Res. 355, Feb. 12, 1998.   More here.

The following relatives may be sponsored by US citizens:   
    * Spouse
    * Children (unmarried and under 21)
    * Sons and daughters (married and/or 21 or over)
    * Parents, if you are 21 or over
    * Siblings, if you are 21 or over
    * Fiance
Greencard holders may sponsor spouse and unmarried children.

Has anyone yet introduced a bill in Congress to change the 14th Amendment to the Constitution to eliminate "birthright" citizenship or has the accepted definition been challenged in US courts? Very unlikely ever to happen.