The Rastriya Prajatantra Party (RPP) has 37 seats in Parliament and its role will be crucial in the 594-strong House for the passage of the bill to address the demands of the agitating Madhesi parties and other ethnic groups.
"Going by the current situation in the House, the bill is not going to get endorsed," Thapa said at the Reporters' Club yesterday.
The Constitution amendment requires a two-thirds majority.
Thapa said that most of the contents and clauses of the bill are not in the country's interest and that unity among parties is vital in this situation. He suggested that the government should seek an alternative to the bill.
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"All political forces should act responsibly to implement the constitution," he said, adding that holding three levels of elections by January 2018 is not possible without the participation of the agitating Madhesi parties.
However, the parties have not come to an agreement about the amendment bill.
The Madhesi Front refused to back the bill, saying it was not acceptable in its current discriminatory form.
The Constitution promulgated last year could not be implemented due to the agitation by the Madhesis.
The Madhesi parties and ethnic groups have been demanding more rights and representation for the marginalised people.
Re-demarcation of the provincial boundaries and citizenship issue are the two major demands put forth by the Madhesis.