They want to demobilize the debate and get the issue off the agenda. That is especially true for Republicans. At the same time, the abortion issue illustrates that the problems of a southernized Republican Party are not simply a matter of how far right the party is. Opinion on abortion has swung sharply toward the Republican position since the controversy over partial-birth abortions began. Even so, polls asking Americans, in effect, which party they trust more on the subject aren't budging.
Many Republican politicians complain off the record about party rhetoric on social issues.
It's not the issue of abortion that's driving people away, they argue, so much as it is the broader cultural claims of those who put it forward. For that reason they are also the main source of radicalization and overreach. From there it was easy for the Republicans to taunt the Democrats into pursuing policies that taxed the patience even of moderate voters. When Americans talk about government spending, about welfare, about crime, about unemployment, or about values, they are to some degree also talking about race. Race is the subtext of American politics.