Those headaches, they say, could override the benefits including lower provisions on their books as fewer loans sour.
The Reserve Bank of India has frequently complained that very few of the country's banks have lowered lending rates despite a 50 basis point cut to policy rates since January.
The RBI left rates unchanged on Tuesday, arguing for the need to allow earlier cuts to trickle down to the broader economy.
Hours after that, market leaderState Bank of India and the country's three biggest private sector lenders announced unexpectedly that they would lower their rates by 15 to 25 basis points.
Bankers expect other lenders to follow that modest reduction: India is a competitive market where nearly four dozen local banks compete for business. But deeper cuts will have to wait, as banks test the impact of the first cut on borrowers.
"If I reduce my rates by half a percent, I don't think you'll rush to take a vehicle loan if you already have a vehicle," said B.K. Batra, a deputy managing director at IDBI Bank which has yet to decide on a lending rate cut.
"It doesn't create any fresh demand -- it may accelerate some demand."
Batra said a rate cut may be an "immediate trigger" for retail borrowers, but not for corporate clients, for whom it is just one of several considerations.
India's slow credit growth has been a headache for banks and for the government, which wants to see faster economic growth.
In the fiscal year to March it was the slowest in almost two decades, according to RBI data. SBI's own credit growth for the year ending in March was less than 10 percent, although it expects a pick up.
"We want to see whether this gives a fillip to credit growth which is what we would like to see. Depending on how that pans out, we will take a call," State Bank of India Chairman Arundhati Bhattacharya said in a television interview, after SBI trimmed its lending rate.
RBI argues that funding costs for banks have dropped, but banks dispute Governor Raghuram Rajan's claim that they are "sitting on money". They say lowering of the key policy rate alone does not lead to a big drop in their cost of funds.
Indian banks derive their largest share of resources from retail deposits, followed by bulk deposits from corporates. They rely least of all on overnight funding from interbank lending or the central bank, where rates have dropped 50 basis points.
They have also kept an eye on margins. Banks including SBI started cutting deposit rates in September, but need to lower that further for more lending cuts without hurting margins.
So far, key deposit rates -- the amount banks pay their depositors -- have fallen by about 50 basis points in the past six months, helping cushion any negative impact on bank margins from the current round of cuts.
But there may be one advantage to lower rates: bringing down costly provisions for loans that have soured. Lower lending rates could revive some debts and help others stay afloat.
UBS analysts estimate a 100 basis point rate cut could help revive 20 percent of the impaired loans.
Banks shouldn't decide rates, markets should: Rajan
'Minimum government, maximum governance' in public sector banks
Is the RBI playing spoilsport for borrowers?
Rate cut will reduce the stress on customers: SBI
How RBI is putting the onus on banks