Update. In my original answer I inadvertently divided at one point when I should have multiplied -- I found the mistake thanks to comments from Frank and THelper. So here's a new tl;dr:
By mile 4,000 at the latest, total emissions from a hybrid Prius beat emissions from a standard Corolla.
Hybrid electric vehicle (HEV) specific components
The HEV components which are not part of a standard internal combustion engine vehicle (ICEV) include:
- Electric motors/generators
- Batteries and/or capacitors
- Electronics (inverter, controller, charger, etc.)
In "Current hybrid-electric powertrain architectures: Applying empirical design data to life cycle assessment and whole-life cost analysis", the authors group the components and make a few assumptions:
- Vehicle construction emissions, excluding the traction battery, are equal for all powertrains.
- Maintenance and disposal (end of life) emissions of all powertrains are equal.
Is ignoring the powertrain a valid assumption?
The assumption that the powertrain construction for all vehicle types has roughly the same CO2 emissions is based on a comparison of battery electric vehicles (BEVs) and ICEVs from "Contribution of Li-Ion Batteries to the Environmental Impact of Electric Vehicles".
Through four different LCA methods (ADP, GWP, CED, and EI 99 H/A) you can see that powertrain (the third pattern from the left) has a similar weight for BEVs and ICEVs:
We can assume that a HEV powertrain would also be roughly the same, as from a component standpoint it splits the difference between the two.
CO2 emissions from battery production
The best data I could find on CO2eq emissions from EV battery production comes from: "Life Cycle Environmental Assessment of Lithium-Ion and Nickel Metal Hydride Batteries for Plug-In Hybrid and Battery Electric Vehicles".
Here are their findings, given as CO2 equivalent emissions per rated watt-hour (Wh) of battery energy capacity:
NiMH: 0.35 kg CO2eq / Wh
Li-Ion (NCM-type): 0.20 kg CO2eq / Wh
Li-Ion (LFP-type): 0.25 kg CO2eq / Wh
These figures match the range found in the report "Life cycle assessment of lithium-ion batteries for plug-in hybrid electric vehicles -- Critical issues" (when scaled from a 10 kWh PHEV battery).
A different report, which is cited (directly or indirectly) in much of the literature on this topic, gives a much lower value for carbon intensity of Li-Ion production:
Li-Ion (alternate): 0.12 kg CO2eq / Wh
From "Life Cycle Assessment of Greenhouse Gas Emissions from Plug-in Hybrid Vehicles: Implications for Policy" (the values themselves are in the supplementary material).
The Toyota Prius HEV comes with either a NiMH or Li-Ion battery bank (from the official spec), with roughly 1.3 kWh capacity (based on a 6.5Ah battery at about 200V - source).
So the resulting emissions for Prius battery production are:
NiMH: 460 kg CO2eq
Li-Ion (average): 300 kg CO2eq
Li-Ion (alternate): 160 kg CO2eq
How far do you have to drive the Prius before it beats the Corolla?
When you drive a Prius off the lot, it has already resulted in emissions of 160 to 460 kg CO2. Per mile, however, it will emit less than a Corolla. So how many miles do you have to drive the Prius before you've emitted less total CO2 than if you'd been driving the Corolla?
From FuelEconomy.gov, a new Prius gets 52 mpg, while a new Corolla gets 31 mpg.
From the EPA, 8.9 kg of CO2 are released for each gallon of gas consumed. So we can calculate the kg CO2eq per mile of each vehicle:
(8.9 kg CO2eq) * 1 / (miles per gallon) = kg CO2eq / mile
Let's call this CO2 per mile or cpm.
Based on the difference in fuel economy, we can then calculate how far you'd have to drive a Prius compared to the Corolla to make up for the CO2 released in the battery production process:
(battery kg CO2eq) / ( Corolla cpm - Prius cpm ) = break-even mile
NiMH battery: 3,967 miles / 6,385 km
Li-Ion (average): 2,587 miles / 4,164 km
Li-Ion (alternate): 1,380 miles / 2,221 km