I believe the root of the objection to a "redefinition of marriage" is that it somehow "lessens" marriage if anybody can do it. The standard Republican argument goes something like this:

1) Marriage is the bedrock of society. It's all about having stable, healthy families.
2) If you redefine marriage to include "non-traditional" pairings, then you (somehow) damage the institution of marriage.
3) Ergo, you're damaging the bedrock of society.

The fallacy in this argument is point 2. The only effect on "traditional" families would be that their children might be somewhat more likely to assume a homosexual lifestyle due to the lower societal stigmatization of such. That particular change has been well underway for decades and is unlikely to ever go back, regardless of any laws passed.