Karen,
If Social Security fails it will not fail in isolation. It will be a catastrophe that will take down every investment market. Basically, whatever our worries about Social Security--- and they are real--- there is greater worry for the future of investment markets. If Social Security is your ONLY source of future income, your income is probably going to be safer than the income of someone who receives both investment income and Social Security benefits.
Indeed, it is that way already. If Social Security is your only source of income today, you are assured of paying no income taxes. But if your income from investments, pension, or IRAs is over certain amounts, your Social Security benefits will be taxed. That's today. The future could see higher tax rates on Social Security benefits for those who have income from other sources.
As a practical matter, you should try a middle path. That would involve one of you taking benefits at age 62 while the other delays until age 68 or 69. For most couples this will optimize benefits. It would also work to help you retain some financial assets and liquidity for emergencies.
Scott