Research has made clear the consequences of unintended/unwanted pregnancies (about 50% of unintended pregnancies lead to abortions). Compared to a planned pregnancy:
[T]he mother is more likely to seek prenatal care after the first trimester or not to obtain care. She is more likely to expose the fetus to harmful substances by smoking tobacco and drinking alcohol. The child of an unwanted conception is at greater risk of weighing less than 2,500 grams at birth, of dying in its first year of life, of being abused, and of not receiving sufficient resources for healthy development. The mother may be at greater risk of physical abuse herself, and her relationship with her partner is at greater risk of dissolution. Both mother and father may suffer economic hardship and fail to achieve their educational and career goals. The health and social risks associated with a mistimed conception are similar to those associated with an unwanted conception, although they are not as great.
What this means is for many people who are already struggling financially, having an unplanned/unwanted child essentially locks them into poverty, and prevents them from elevating their social standing, abridging their educational pursuits and relegating them to low-wage, low-status jobs - if they are employed at all. Research has found that women in the US were less likely to have full-time employment six months after denial of abortion, with public assistance programs playing an important role in mitigating the loss of that employment (even though the assistance did not make up for the added financial strain of having a child).
The single most common reason women cite for wanting an abortion is because they cannot afford to raise a child, Foster said.
For women denied abortions, public-assistance programs failed to make up for the cost of a new baby and to pull households out of poverty ...
"Women who were refused abortions were nearly four times as likely to live below the federal poverty line four years later as women who had abortions, the researchers found." Source
So the important point from all of this is that the majority of women looking to receive an abortion are doing so because they do not have the financial resources to care for the child. For women who are denied abortions, carrying the child to term places even more financial hardship onto them, with public assistance programs being absolutely crucial for financial support (as meager as they are).
So why would Republicans, who are actively trying to gut public assistance programs at every turn, want policy that ensures more single mothers who are dependent on said programs? Because we've been here before. The term "Welfare Queen" entered public discourse in the 1970s, where isolated instances of welfare fraud were amplified to the point where it became a stereotype of single (usually black) mothers. Reagan used one of these isolated instances on the campaign trail in the mid-1970s to paint public assistance programs as wasteful and prone to abuse, and that we were becoming a "welfare state" - this mindset of "personal responsibility" is what helped paved the way for the welfare reforms of the 1990s. An influx of mothers dependent on public assistance would, like it always has, be painted as wasteful government spending on irresponsible mothers, and used as an argument to further erode our public assistance programs.