A Mech. Inf unit with Garrison 3 which has been fortified for 5 turns gets +100% bonus when defending - at a strength of 64. To this must be added any bonuses from city and tile defence, making it a formidable opponent. You should, naturally, batter the city-defence down to zero by bombardment, but there's no way to cut down tile defence for which the bonuses are also cumulative: I met with trouble when my enemy had thoughtfully built a city on a hill/forest/jungle tile for a tile defence of +125%, which would have added another 32 points to a mech. inf. Until that moment, I had nor realised that such 'compound' terrain features would have such a powerful effect, nor even that a threefold condition existed.
As stated by others, bomb and strafe to whittle them down. And your own units will do better with some promotions, don't forget: City Raider 3 gives your Modern Armour a city-attack strength of 40 +75% = 70, plus any Combat promotions. Or go for Flanking and use a hit-and-retreat tactic, again wearing down the enemy. (The latter is also true for Artillery attacking units, but alas not for bombarding).
Even with the two attacks allowed by Blitz, which all Mod. Arm. gets at the outset, it seldom happens in my games that each one of my units destroys one or more of the enemy units in a well-defended city during a single turn. So you need to outnumber him, as well as out-strengthing him, to avoid a lengthy siege. Bring up a good big force.