Objection to the amendment, which says that parishes that object to the episcopal ministry of women can request a male bishop, led to the Measure's rejection at General Synod in July.
The House of Bishops, which had added the amendment, is revisiting the Draft Measure to try and establish a compromised form of legislation before the next General Synod.
But while the House of Bishops, in a subsequent discussion document, outlined three options - to retain the amendment; to remove the amendment; and to replace the new amendment with a different provision - some groups are urging the House to drop provision for dissenting parishes completely.
The Group for Rescinding the Act of Synod (GRAS) said in a statement today: "The Church of England risks finding itself in a position where people who long to see women and men as bishops together will vote against the Measure, because the compromises it makes would be too damaging to the Church and to our theology of the place of men and women in creation."