Pakistani Islamists are demanding the government leave the country's laws against blasphemy alone.
Thousands rallied in Karachi and other cities Friday to warn government officials any effort to repeal the laws would have serious consequences.
Several Pakistani lawmakers proposed changing the law after last month's conviction of a Christian mother of five for blasphemy against Islam.
Asia Bibi is the first woman condemned to die under Pakistan's blasphemy law. She denies claims by local women that she made derogatory remarks about the Prophet Muhammad.
Pakistan's Minister for Minority Affairs Shabaz Bhatti has recommended Bibi be pardoned or released if her pending court appeal is not quickly addressed.
One Pakistani cleric has said if the government fails to go ahead with the hanging, his mosque will offer $6,000 to anyone who kills her.
Convictions under the law are common, but no executions have ever been carried out.
Protest leaders are calling for a nationwide strike if the government tries to heed calls from the West to change the blasphemy law.
Pakistan's Christians, who make up less than 5 percent of the country's 175 million people, have long complained of discrimination. Christian and human rights groups have expressed shock at Bibi's death sentence and have begun an online petition calling for Pakistan's blasphemy law to be repealed.
Some information for this report was provided by AFP.