"How exactly will the extension to homosexuals of the right to civil marriage have any effect on the stability of child-producing heterosexual marriages on which society depends for its future?"
Jon mentions the "right to civil marriage" above, but of course, every right comes with a responsibility. In the marriage contract between a couple and society the couple assumes the responsibility to welcome children, raise them in a manner that will enable them to become full, contributing members of society. If we extend the benefit of marriage to those who do not share the responsibility for bringing in new contributing members of society then we cheapen the benefit.
In the case of monetary benefits, the pool available for those benefits is finite. If we increase the numbers who are eligible for those benefits, then everyone currently receiving those benefits must accept a decrease in that benefit. Each decrease in that benefit represents a step back by society from its obligations in the marriage contract.
Today, society has neglected these obligations so badly that the benefits that society affords to married couples are almost negligible. This has weakened the marriage bonds between married men and women (resulting in divorce) and between couples and society (resulting in cohabitation, etc.) with devastating effect. Rather than just conceding defeat, I believe now is the time to begin the process of increasing society's support for marriage.