Together, these developments “highlight the political problem that could be caused if we were to nominate someone like Ted Cruz at the top of the ticket,” said Brian Walsh, a Republican consultant and former adviser to House and Senate leaders, who has not endorsed a presidential candidate.

“In the last several elections, the Democratic playbook has been to discuss the ‘war on women’ narrative” against Republicans, Mr. Walsh said. “If you have a much more polarizing ideologue like Ted Cruz at the top of the ticket, you would make it that much easier for Democrats to prosecute that argument.”

Karl Rove, a Republican strategist and a former top adviser to President George W. Bush, has called proponents of shutting down the government to defund Planned Parenthood the “suicide caucus”; party leaders are well aware that Republican attacks on the organization back to the Clinton era have not ended well for Republicans. On Tuesday, the House Democrats’ campaign organization attacked Republicans in 18 House races, asking in news releases whether the candidates still supported the “now indicted conspirators behind Planned Parenthood videos.”

Nonpartisan opinion polls suggest Republicans are right to be concerned.

A majority of Americans continue to support Planned Parenthood and its federal payments, which reimburse nearly 700 affiliates for providing reproductive care, preventive health services and treatment of sexually transmitted diseases to low-income Medicaid recipients. Payments for abortions, which are performed by a little more than half of Planned Parenthood centers, are prohibited by federal law except in cases of rape, incest and a pregnancy’s threat to a woman’s life.

A survey for The New York Times and CBS News this month showed that nearly six in 10 Americans say Planned Parenthood should receive federal funds. That finding was statistically unchanged from a similar survey in September, even as conservatives at the local, state and federal levels stoked outrage about the videos from a group called the Center for Medical Progress, founded by a 27-year-old Californian, David R. Daleiden, one of those indicted Monday.