Merkel's Bavarian sister party CSU had on Monday already given her an ultimatum to curb migrant arrivals or risk pitching Germany into a political crisis that could rattle Europe.
But the CSU now also take issue with an agreement announced Tuesday by Germany's and France's leaders to set up a common budget for the eurozone which will fund investments in poorer member states.
"We were always very sceptical about a eurozone budget. Simply because it's a form of additional budget," Bavaria's state premier leader Markus Söder told Süddeutsche Zeitung.
"Is it separate from the German legislature? Does it mean that the fundamental stability of the euro will be challenged? All that must be clarified," he said.
Ahead of a meeting with Austrian Chancellor Sebastian Kurz in Linz on Wednesday, Söder confirmed that his party will call a coalition panel to examine the issue.
Germans are deeply opposed to any "transfer union" that sees their taxes flowing to eurozone laggards.
And Merkel herself had initially appeared lukewarm to the idea of a budget for the bloc.
But she has since offered a key concession in backing French President Emmanuel Macron's call for such a fund.
However, she said in a recent interview that the total sum should be at the low tens of billions range -- far less than what Paris had hoped for.
‘Don't mix finance and asylum'
The CSU's attack on the eurozone reform proposal came in a week already marked by a deep rift between the Bavarian party and Merkel over her liberal refugee policy that allowed more than a million asylum seekers to enter Germany since 2015.
Merkel's decision had proven divisive, and voters in September's elections handed her her poorest score ever and gave seats for the first time to the far-right anti-Islam AfD.
Several high profile crimes by migrants -- including a deadly 2016 Christmas market attack by a failed Tunisian asylum seeker -- have also fuelled public anger.
Germany's Interior Minister Horst Seehofer of the CSU has been one of the fiercest critics of Merkel's refugee stance.
The frustration tipped over on Monday, when he gave Merkel a fortnight to find a European deal to curb new arrivals by a June 28-29 EU summit, failing which he vowed to order border police to turn back migrants.
Coming to Merkel's rescue on the explosive issue of immigration, Macron on Tuesday said after talks with her that Paris and Berlin have agreed to seek an EU deal to send back migrants registered elsewhere in the bloc.
The German leader had earlier suggested that deals could be struck with other EU countries in return for financial or infrastructure support.
But Söder warned Merkel against mixing European finance and asylum policies by offering European partners financial incentives in exchange for cooperation on migrants.
"They are two different areas. There must be a clear principle of the rule of law," he added in Linz on the Danube river.