The process, also known as "bracket creep" and often described as a "secret tax hike", occurs when taxes rise faster than income in real terms, as tax rate thresholds do not take account of inflation.
The rebels have called for the government to act during this parliament to ease the burden on taxpayers, just over a week after new figures showed German workers were paying record amounts in tax.
On Thursday, the economic wing of CDU called for a new tax system in which the rate thresholds would be automatically adjusted annually to take inflation into account.
Merkel made clear before parliament broke for summer that she had no plans to change tax rules. There was said there was "no room for manoeuvre in fiscal planning, also not in the area of tackling cold progression".
Rebellion in the ranks
Ruling junior coalition partner the Social Democrats (SPD), a centre-left party traditionally in favour of raising taxes, also said on Friday they would join the CDU rebels in calling for a fight against cold progression - as long as the government would continue to receive the same amount in tax revenue.
The SPD offered to enter urgent talks with the CDU/CSU on the issue, said Johannes Kahrs, the Social Democrat's parliamentary spokesman on budgetary policy.
Meanwhile, the CDU's workers' wing (CDA) has said it plans to draw up a joint proposal with the party's Mittelstand representatives - small and medium-sized businesses - for discussion at the party conference in December.
"The secret tax hikes are a burden on our workers," CDA head Karl-Josef Laumann told the Rheinische Post on Friday, but he added he did not want tax cuts to lead to a loss of government revenue.
One suggestion the CDA has put forward to make up any budget shortfall caused by tax cuts for the lower paid was to raise taxes on those who earn over €250,000 a year from 45 percent to 49 percent, Handelsblatt reported on Friday.
SEE ALSO: Conservatives: We'll lower taxes too