This is becoming apparent in view of factors, like the Left parties finding the situation caused by Prime Minister Manmohan Singh's decision to put on hold the process a golden opportunity to press consideration of its alternative proposals.
Besides, a key ally Lalu Prasad-led RJD has come out in strong support of the DMK, whose threat to pull out of the UPA government if the divestment in the Neyveli Lignite Corporation went ahead, prompted the Prime Minister to put on hold the process.
A section of Congress is itself saying that an immediate forward movement on the matter is ruled out also because of the fact that the panchayat elections in Tamil Nadu are scheduled in the next few months.
DMK would not like any progress on the divestment matter in the next few months, lest rival AIADMK exploited any controversy and created problems in the panchayat polls.
While there has been no official word about the next UPA-Left Coordination Committee meeting, it is expected on July 22, two days before the monsoon session of Parliament which is likely to be a stormy affair.
The Congress has officially said that economic reforms would continue. But a section in the party is subtly pointing out that reforms do not mean divestment alone.
The Left parties, which were the first to force the government last year to put the controversial BHEL divestment decision on hold, feel that the time was ripe for seeking a response from the government on their alternative proposals for resource mobilisation.
This is also in the backdrop of government statements that funding for key programmes like rural employment guarantee programmes could get affected if the divestment issue remained in limbo for long.
The BHEL controversy had seen the first major rupture between the Congress-led coalition and the Left parties, who had then suspended attending the UPA-Left Coordination Committee meetings.
A Left leader said that they would take the opportunity to hold threadbare discussions on all issues raised in their note on the two-year performance of the UPA government and would also like consultations on a case-by-case basis on divestment.
A leader from a non-Congress UPA constituent, however, said the divestment issue would be brought back on the rails again in few months.
The problem is not with divestment, but with the manner it is done, he said, adding Karunanidhi should have been consulted at the political level before a decision on Neyvelli.
The thinking in the Congress leadership is that the matter needed to be handled patiently by holding more consultations at various levels in a spirit of give and take.
Though the decision to put on hold the divestment was a setback for the coalition, it is not unduly worried about its adverse impact on the stability of the government as its perception was that no partner wanted to sink the ship.
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