One of my favorite things about AskHistorians is when someone asks a question that seems fairly straightforward but is wonderfully complicated once you lay it out and look at its different parts. To tackle the big picture first, this great response from u/amandycat to a question about grief and the loss of a child gets at the short answer. One section, in particular, speaks to what you're asking [bolding mine]:

Your question asks how it would be possible to cope with such losses, and to some degree that question can’t really be answered, because the truth of the matter is that responses to grief were as individual as they are now. There are a few reasonably cut-and-dried answers to be had which might satisfy, though. One of the responses to this is that in societies with a high mortality rate, the risks of pregnancy, childbirth and childhood itself are expected, and the consequences well-known. The death of a child is still regarded as a tragedy, but it is not one which is painfully unexpected or isolating as it is now. Where now, bereaved parents are likely to have to actively seek out others who have shared experiences, this would not have been the case in early modern England.

The connection to your question lies in the bolded text: people's responses to all aspects of pregnancy were as individual as they are now. I can't speak to other countries but can say that in America, the nature of a person's response to pregnancy was shaped by a number of factors, including their race, class, and social status and there aren't a lot of straightforward answers but I can offer a few. (Much of my answer is shaped by the research I did for our recent MM on the history of abortion in America, which is part of the history you're asking about.)

Despite the individual nature of how someone would feel upon learning they were pregnant, there are some universal experiences that are worth clarifying. Most notably, the idea that a missed period = pregnancy is a fairly modern construct. Confirming a pregnancy without a lab test that early wasn't possible until Margaret Crane invented the home pregnancy test in 1967. Even then, it was almost a decade before such tests were available (more on Crane here.) Before that, people who suspected they were pregnant and wanted official confirmation had to consult a doctor and get blood or urine analysis.

Before that, a person who could get pregnant typically couldn't confirm they were pregnant until they felt the fetus move, usually around four or five months after the embryo implanted in the uterus. This sensation, known as "quickening," was generally accepted as evidence of a viable pregnancy until the mid to late 1800s. Before the quickening, the lack of a period was described as "blocked menses" and could reflect an illness, a body out of balance, an insufficient diet, weight loss, or possibly a pregnancy.

Which is to say, a pregnant person didn't become an expectant mother immediately after the first missed period until very, very recently. If we slide away from the universal, back towards the individual, we can start to see all of the possible exceptions to this and how individuals may have felt. When we're talking about white women in American history, it's helpful to consider what historians describe as the "great fertility decline" that began during the American revolution and saw a dramatic reduction in the number of children white, American-born women had. From Susan Klepp's foundational text on the topic (Revolutionary conceptions: women, fertility, and family limitation in America, 1760–1820):

The Signers of the Declaration of Independence came from large families. Those who were delegates to the Second Continental Congress in 1776 came from families with an average of 7.3 children.... And, just eleven years later, those founding fathers who met once more at Philadelphia, this time to draw up the Constitution of 1787, produced an average of just 4.9 (legitimate) children over the course of their lives, quite similar to the record of the members of the first Supreme Court (who had an average of 4.8 children) and the first president, vice-president, and Cabinet secretaries (who averaged 5.1 offspring).

There are any number of theories as to why it happened (both physically and socially speaking) but how an individual white person felt about a pending pregnancy was likely linked to their feelings about the nature of womanhood and her responsibility to bear children. That is, if she believed in limiting births and discovered that her efforts to prevent pregnancy were unsuccessful, she was likely disappointed. Conversely, if the person was eager to have as many children as possible, the confirmation of a pregnancy was likely met with celebration. Meanwhile, Lara Freidenfelds's work on the history of miscarriage includes writing from pregnant people expressing concern or fears about pregnancy based on their previous experiences with giving birth or bearing witness to the delivery experiences of other women around them. Sometimes these fears, or disappointment in a suspected pregnancy, led them to pursue a cure to their "blocked menses" and the elimination of the pregnancy.

My hunch is that part of your question is getting at if people were more afraid of being pregnant when they thought there was a possibility they would die during delivery or their fear their baby would die. My sense is it's more likely that throughout American history, a white pregnant person's feelings about a pregnancy were more closely linked to their feelings about childbearing, being pregnant, or being a parent than to the support available to them at the time of delivery.

However, at this point, there's no more way to avoid it - we have to confront the history of modern obstetrics.

There is a lot of ugliness in American history that impacts us in the modern era in ways big and small but few of them linger in our daily lives in the way the history of gynecology and obstetrics do. That history is why it's so important to differentiate the experiences around pregnancy for white and Black women and girls. There are a whole bunch of exceptions based on class and geographical location, but loosely speaking, white women before 1900 or so experienced pregnancy and delivery as a collective experience with other women, especially at the moment of birth. (These linked responses from /u/mimicofmodes gets at how women dressed during pregnancy and what "confinement" meant for upper-class women.) That same wasn't true for Black women and girls, especially before and during the Civil War.

Beginning in the 1820s, education in America went through a process of "feminization" - teaching was repositioned in society as a women's work, the schoolhouse was treated as an extension of the home, etc. The opposite happened with regards to midwifery and gynecological care. In effect, what had been a feminized trade, was masculinized. The practice was taken out of the home and moved to the doctor's office or the hospital. The practitioners shifted from women with lots of hands-on training to men with formal, classroom training. And a great deal of the training happened at the expense of Black women's health and safety. A prevailing and deeply racist sentiment of the era was that Black women felt less pain than white women and as such, could handle invasive medical procedures or treatments without needing anesthesia. These sentiments were rooted in the racist assumption that enslaved Black women and girls' primary function was to give birth and to, in effect, create new slaves. This was codified through laws like Virginia's policy of partus sequitur ventrem - that which is born follows the womb - which meant a child's legal status came from the person who gave birth to them. In effect, a child born to an enslaved girl or woman belonged to the person who owned her. Deidre Cooper Owens' book, Medical bondage: race, gender, and the origins of American gynecology is worth reading in full and explores several threads that came together to create the medical fields of gynecology and obstetrics and one of them was an interest among enslavers in the American South who wanted to ensure healthy, safe deliveries among the people they enslaved and ensure multiple pregnancies. As there is no meaningful difference between white bodies that can get pregnant and Black bodies that can get pregnant, many of the treatments developed on enslaved women were later used to save the lives of white women. (A smidge more on that history here from /u/zaxina.)

So, to circle back to your question: a married white, upper-class, urban woman eager to start a family in the late 1800s may have felt more comfortable with being pregnant knowing that if something went wrong, she'd have easy access to a trained, medical professional. But the greatest impact on her feelings was likely her own thoughts on motherhood and pregnancy. Meanwhile, the feelings of an expectant enslaved Black woman in the early 1800s - during the development of modern obstetrics - were compounded by her status, the baby's father, and the degree to which future obstetricians would be interested in her pregnancy, her delivery, and her body.