The shift by N Chandrababu Naidu, chief minister of the southern state Andhra Pradesh, came six weeks after Modi announced to a stunned nation that he would scrap 86% of the cash in circulation.
While Modi remains by far India's most popular politician, any crack in his authority could have negative implications in state elections next year that will set the tone for his expected bid for a second term in 2019.
Naidu's regional party is allied to Modi's nationalists and he heads a federal committee set up to find ways to soften the impact on ordinary people of the crackdown against tax evaders, racketeers and bribe takers who rely on so-called "black cash".
"I am breaking my head daily but we are unable to find a solution to this problem," Naidu told party workers on Tuesday in the city of Vijayawada.
Modi, announcing the reform on November 8, cautioned that people would face temporary hardship. He promised to restore normalcy by the end of the year, when a deadline to deposit old 500 and 1,000 rupee banknotes expires.
His announcement enjoyed popular support at first, with many people prepared to endure hardship as long as others are forced to give up their ill-gotten wealth or pay tax.
But continuing shortages of new 500 and 2,000 rupee notes have caused tempers to rise as millions queue at banks and ATMs to draw money. With new 500 rupee notes, worth $7.50, in very short supply it is hard for people to buy necessities because of a shortage of change.
"Modi is now a one-man army, every political ally will blame him if the cash crisis does not come to an end in the next 10 days," said P Raja Rao, a political science professor in Hyderabad.
Furious over the lack of cash, mobs attacked six bank branches in Uttar Pradesh on Tuesday, forcing police to rescue bank staff.
The northern state, home to one in six Indians, is due to hold an election in early 2017 that is increasingly being viewed as a referendum on Modi's demonetisation drive.
In the last 20 days, Modi's Bharatiya Janata Party (BJP) has won several local elections in western and northern states. Party officials said the wins were a clear endorsement of the new cash policy.
"Each and every Indian understands the genuine intention behind the bold move. They trust the prime minister and we hope our political allies put an end to their doubts," said BJP spokesman Siddharth Nath Singh.