Among other things,opponents contend that the bill fails to provide any assured return to subscribers.
Trinamool Congress parliamentary party leader and union minister Sudip Bandopadhyay told HT from Kolkata on Sunday, "Reforms in areas that affect common people are critical issues. In the case of the PFRDA Bill, our leader Mamata Banerjee has not yet decided if we will support it."
Another union minister from the party, Saugata Roy, told HT: "As it relates to lifetime savings of common people, we have certain reservations about it."
The Congress, however, did not seem perturbed.
"If our allies have any apprehensions, we will definitely talk to them and sort out the issues. This is a key bill," said a Congress minister.
While the Centre sees the PFRDA as a major reform-related legislation and is keen to pass it during the winter session of Parliament, the Left parties have already raised their red flags.
While the row over FDI in retail stalled Parliament all of last week, the CPI-M's trade union wing, CITU, led a delegation to meet Prime Minister Manmohan Singh to ask for drastic changes in the PFRDA Bill, including a provision for minimum assured return for investors.
The union cabinet recently approved the PFRDA Bill but ignored the recommendation of Parliament's standing committee on finance to keep a 26% FDI cap within the legislation.
While the UPA managers want to keep the FDI limit out of the law to allow changes in it through executive orders, the proposed legislation has also irked a section of the BJP.
The CPI-M's Basudeb Acharia told HT, "We are trying to garner support from other political parties against the PFRDA Bill. We will force voting on the bill if the government tries to pass it in this session."