As Gallup discusses here, initial reaction to Roe v. Wade was more neutral than anything: the majority of people felt that it was "legal only under certain circumstances" as opposed to roughly equal numbers of people feeling either strongly opposed or strongly in favor of. I do not know how long the issue of abortion had been in the public consciousness, but as far as a more detailed description of the growth of Roe v. Wade as an important issue among conservatives and the Republican party, the only book I've read in recent memory addressing Roe v. Wade specifically is Rick Perlstein's The Invisible Bridge; his writing is better than my summary, so I'll just quote it at length here.

...Supreme Court justices... two days after the re-inauguration of Richard Nixon in 1973 ruled that no state could restrict any abortion performed in the first three months of pregnancy, and severely limited states' ability to regulate abortions performed after that. Here was a procedure so controversial that the archbishop of Los Angeles had pronounced in 1970, after California passed a law that let women terminate pregnancies with little more than a doctor's note claiming childbirth would cause emotional distress that Catholics "excommunicate themselves from the church by cooperating in any way in abortion, even counseling one."

At first, the Roe v. Wade backlash was mostly limited to Catholics. (Opening sentence to following paragraph, separated for emphasis.)

The attorney who represented the pro-choice side was a member of god standing of the Southern Baptists, a denomination that, at its 1974 convention, tabled an antiabortion resolution and reaffirmed one approving abortion in cases including "evidence for likely damage to the emotional... health of the mother. The American Baptist Association, going further, endorsed what critics called "abortion on demand." But more fundamentalist Protestants were soon raising their voices, too. At the American Baptist convention, a minister's wife from Arkansas thundered from the floor that abortion was "nothing less than legalized murder of masses of human lives." Christianity Today, Billy Graham's trade magazine for evangelical ministers, formerly ambivalent, even indifferent, on the issue, now editorialized that abortion "ought not to be regarded as a Catholic issue because the Catholic leaders oppose it," and that since the fetus was a "human person," abortion was "manslaughter, if not murder." When the National Right to Choose Committee organized in Detroit, the members chose a Methodist, Marjory Mecklenburg as their first chair. In April of 1974, fifteen thousand activists bearing signs reading DON'T MAKE THE WOMB A TOMB and ABORTION-HITLER'S FINAL SOLUTION, many of them young parents with sign-toting children in tow (I'M ADOPTED. I'M GLAD I WASN'T ABORTED), gathered for a silent cadence. Silent, that is, until the speeches began. Congressman Lawrence Hogan, cosponsor of the "Human Life Amendment" to override Roe, boomed, "We as a nation have denied the most basic right of all-the right to life." Mecklenburg said that "seven arrogant and callous men"-the Supreme Court majority-had "brought America into the most destructive war in the history of mankind,... a war in which the toll of American lives will be many times greater than in World War II." And some people didn't even care!

For many it was the very antidemocratic nature of the Supreme Court that made its decision so galling. "Abortion is the monumental sort of issue over which wars are fought," a letter writer huffed angrily in the Hartford Courant that August, but it somehow had been disposed of once and for all in secret by unelected judges. "It is strange indeed that the major media and politicians have long tried to cover up discussion of this vital issue. I wonder why?"

These quotes come from page 300-301; later on, in page 443, the issue is revived when Perlstein discusses "the right-wing insurgency bubbling barely beneath the surface-what conservative referred to, like civil rights activists from the 1960s, as "the movement."

Activists in the "pro-life" cause (James Wolcott of the Village Voice helpfully explained that the unfamiliar referred to those fighting against abortion) had been thick on the ground at CPAC [Conservative Political Action Committee]. A month before that convention, what Christianity Today called "an unexpectedly large turnout" of twenty-five thousand braved the winter chill for the second annual "March for Life," commemorating the Supreme Court's Roe v. Wade decision. The previous year's demonstration had drawn only what the AP had estimated as "hundreds." ... A Catholic senator, James Buckley, and an evangelical one, Mark Hatfield, introduced a resolution the week of the Roe anniversary to extend "the right to life-to all human beings including their unborn offspring." Shortly after, Buckley was joined by the very conservative Southern Baptist, Jesse Helms of North Carolina, to propose the same language as part of a constitutional amendment banning abortion.

Further, on page 492, he discusses Betty Ford, Gerald Ford's wife, getting flack for referring to Roe v. Wade as a "great, great decision." While liberals and moderates tended to applaud her decision, as Perlstein presents it, she got shredded by the more Reaganite segment of the Republican party.

Source:

Rick Perlstein, The Invisible Bridge