Joachim Herrmann from the Christian Social Union (CSU) started the debate on Sunday while commenting on concerns that foreigners would avoid shopping in Germany if they have to pay to drive there.
Under the plans, foreign drivers will pay to enter Germany, raising millions of euros to fill the blackhole in the country’s infrastructure budget.
"To dispel concerns in the border regions, an easy arrangement should be considered: All districts along the border… could be excluded from the toll," Herrmann told the Welt am Sonntag newspaper.
But Bavarian state premier Horst Seehofer (CSU) quickly rejected his minister's idea.
Not everybody needed to "butt in" while Transport Minister Alexander Dobrindt (CSU) was finalizing the toll plans, Seehofer said.
"Alexander Dobrindt will take his time to work on a bill. And once that is on the table it will make sense to discuss it," the CSU leader said on Sunday to broadcaster ARD.
Despite his party leader's rebuke, Herrmann defended his proposal in an interview with the Süddeutsche Zeitung on Monday.
"I want the toll. But we have to talk about those things [exemptions] if we are doing the fine-tuning now," he said.
The centre-left Social Democrats (SPD), who form a coalition with Chancellor Angela Merkel's conservative Christian Democrats (CDU) and their Bavarian sister party CSU, have been sceptical of the toll all along.
The chairman of parliament's transportation committee, Martin Burkert (SPD), signalled he was open to Herrmann's idea.
"We have to talk to the neighbouring countries," the MP said. "Tourism and shopping in the border region are especially threatened [by the toll]."
"If he [Dobrindt] does not get it done, we Social Democrats will be the last ones to stand in the way of dropping the plans,” Burkert told the Welt newspaper.
Dobrindt's 'double trap'
Dobrindt introduced his plan, which is a key CSU project, two weeks ago, but key details remain undecided.
The CSU hope to avoid legal action over accusations the plan discriminates against foreigners by charging everyone, but then cutting the amount of road tax Germans pay. That will, however, require a huge amount of bureaucracy.
And Finance Minister Wolfgang Schäuble (CDU) questioned in an interview with the Rheinische Post on Saturday whether officials would be able to send out 50 million car tax bills to German drivers by 2015, which would be needed to introduce the toll.
The parliamentary leader of the ecologist Green Party, Anton Hofreiter, said Dobrindt was "caught in his own double trap".
"If all trips foreigners now make on all German roads are taken into consideration, like the transport minister plans, this would be a de facto entry free to Germany. That would ultimately hurt the economy of all border regions," he told the Straubinger Tagblatt on Monday.
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