NASA wants to use a derivative of the SSME for the 2nd stage engine. However, the SSME was designed to be started before the solids are ignited, not an air launch. Apparently, there is some problem with assuring the ignition sequence will properly fire while in flight. In the history of the Shuttle program, there were a few cases where the launch was aborted at the last second (literally) when a problem was detected with the SSME startup sequence. On the pad, that is an inconvience. In flight, you've probably got an abort situation, especially if there is only 1 engine (I think that's what they're wanting for the CEV 2nd stage).

The J-2 was a good engine with a proven in-flight start and restart capability. They were used in the upper stage of the Saturn IB, and 5 of them were used on the Saturn V second stage and 1 was used for the third stage. It isn't as powerful or as efficient as the SSME, though.

Manufacturer Name: J-2. Designer: Rocketdyne. Developed in: 1960. Application: . Propellants: Lox/LH2 Thrust(vac): 105,352 kgf. Thrust(vac): 1,033.10 kN. Isp: 421 sec. Isp (sea level): 200 sec. Burn time: 475 sec. Mass Engine: 1,438 kg. Diameter: 2.01 m. Length: 3.38 m. Chambers: 1. Chamber Pressure: 30.00 bar. Area Ratio: 28. Oxidizer to Fuel Ratio: 5.5. Thrust to Weight Ratio: 73.1801112656467. Country: USA. Status: Out of Production. First Flight: 1966. Last Flight: 1975. Flown: 87.

Used in Saturn IVB stage in Saturn IB and Saturn V, and Saturn II stage in Saturn V. Specific impulse and thrust is for final flight version; J-2 had a specific impulse of 418 sec/thrust of 90,700 kgf/mix ratio of 5.00 on LV's SA-201 through 203, and 419 sec/thrust of 102,040 kgf on SA-204 through 207 and SA-501 to 503.

The numbers for the baseline SSME are as follows:

Manufacturer Name: RS-24. Designer: Rocketdyne. Developed in: 1972. Application: . Propellants: Lox/LH2 Thrust(vac): 232,301 kgf. Thrust(vac): 2,278.00 kN. Isp: 453 sec. Isp (sea level): 363 sec. Burn time: 480 sec. Mass Engine: 3,177 kg. Diameter: 1.63 m. Length: 4.24 m. Chambers: 1. Chamber Pressure: 204.08 bar. Area Ratio: 77.5. Oxidizer to Fuel Ratio: 6. Thrust to Weight Ratio: 73.1197829645898. Country: USA. Status: In Production. First Flight: 1981. Last Flight: 1998. Flown: 279. References: 225 . Comments: Used in Shuttle Orbiter. Space Shuttle Main Engine. Staged combustion, pump-fed. Originaly specification was vacuum specific impulse of 455, but not achieved in the final design.

The key numbers are:
Thrust (vac)
J-2: 105,352 kgf., 1,033.10 kN
SSME: 232,301 kgf. Thrust(vac): 2,278.00 kN

It appears you could use two J-2s and get nearly the same thrust as one SSME. Two J-2s would be larger than a single SSME but have a slightly lower mass. I don't have the numbers to back it up, but I'm pretty sure that the vacuum Isp for the SSME is significantly higher than for the J-2, something on the order of 20 seconds or so. This is due to the chamber pressure being so much higher on the SSME (almost 7 times higher). The SSME's higher Isp would more than offset its higher mass if propellant mass. Perhaps it's the combination of slightly lower thrust and lower Isp that makes NASA think the J-2 is not quite what they need for the CEV second stage. However, since the J-2 has been out of production for 30 years, perhaps they could upgrade it a bit to improve performance. The 5 segment SRB might be able to make up for some of the J-2's perceived shortfall.

Alternatively, perhaps there's another LH/LOX engine out there already in production. I don't have the time to do an extensive search, but here are the numbers for the Vulcan 2 engine used on the Ariane V. The numbers are as follows:

Designer: SEP. Propellants: Lox/LH2 Thrust(vac): 132,563 kgf. Thrust(vac): 1,300.00 kN. Isp: 434 sec. Isp (sea level): 318 sec. Mass Engine: 1,800 kg. Diameter: 2.10 m. Length: 3.50 m. Chambers: 1. Chamber Pressure: 116.00 bar. Area Ratio: 61.5. Oxidizer to Fuel Ratio: 6.7. Thrust to Weight Ratio: 73.6461709372948. Country: France. Status: In Production. First Flight: 2002.

Perhaps two of those engines could power the CEV second stage but I don't know about its in-flight start capability. There could be other suitable engines already in production but I don't have time right now to look for them.