First, there are serious financial disincentives for people on public assistance to marry. The Department of Health and Human Services sets poverty guidelines based on family size. These are used to determine eligibility to Head Start, Food Stamp Program, the National School Lunch Program, the Low-Income Home Energy Assistance Program, and the Children’s Health Insurance Program. They are also inform the guidelines that state and local governments use for access to their programs. Unfortunately, these guidelines make it costly for very poor people to marry. A single working mother with two children counts as a family of 3, which in 2011 would be defined as in poverty at an income level below $18,530. If she were to marry, she would be part of a family of 4, but the poverty level only increases to $22,350. Let's say the that a father is in the picture, and each of the couple can earn $12,000 a year. If the couple marries, they could lose access to public support, decreasing their combined income. If the father wants to contribute to the family income, he will contribute more by supporting his children and their mother financially, but not getting married. The policies built into our safety net are a far bigger "marriage penalty" than anything in our income tax law.
Second, the criminal justice and public benefits systems have become entwined in a way that makes many poor people outcasts from the marriage market. If one has a felony convictions, particularly for drug possession, one is often barred from public housing and other benefits. Drug laws are selectively enforced, and poor people are far more likely to be arrested, tried, and convicted than wealthier people who commit the same crimes. In some urban areas, up to half of all men have been convicted of a drug crime. If these ex-convicts were to marry and move in with their significant others, their whole family could be evicted from their homes.
Third, the poor don't have the same financial incentives to marry as wealthier people do. Traditional marriage law is designed to protect the joint wealth of a couple. If one person should pass away, their health benefits, insurance, and assets are still controlled by the spouse. This financial benefit explains why wealthier people still get married, even when many complain that the tax code penalizes a couple for having two incomes. Poor people often don't have any wealth, insurance, or benefits to pass on to their loved ones. Therefore, there are no financial benefits to overcome the aforementioned penalties.
If conservatives were truly concerned with strengthening families, they would remove obstacles to poor people marrying. They would adjust the eligibility requirements for public benefits to reduce the penalty for adding an income-earner to a household. They also would stop making social outcasts of people who have paid their debt to justice by serving their prison terms.
Alas, I don't think that they will advocate these kinds of changes soon. It serves a conservative narrative to portray the poor as victims of their own moral failings. Doing so justifies the continued prosecution of the War on Drugs, with its attendant financial advantages to police departments, suppliers of military-grade equipment, and private prison contractors. The narrative also justifies eroding the social safety net, which must happen to fund the tax cuts their wealthy supporters have obtained.
No, poverty is not caused by a breakdown in family values. The breakdown in the family is caused by the policies that we inflict on the poor, and these policies are part of a circular effort to justify the policies that we inflict on the poor.