First of all, weight lifting more often is not going to have much of an impact on weight loss. It's not an efficient way to burn calories and you're better off using standard "cardio" (running, biking, etc) if you're trying to achieve a caloric deficit. The primary use of weight lifting while cutting is to help maintain LBM, which is also extremely important, but it's usually enough to just lift heavy ~3 times per week to achieve this.
Second, I would not recommend lifting heavy with the same muscle groups every single day. If you do a 4 or 5 day split routine that works different muscles every day, you'll be fine, but if you work out your entire body every single day, you're likely to fail. Your muscles need time to rest, but just as importantly, so does your CNS. If you do more weight/volume/intensity than your CNS can recover from, not only will your results slow, but you may experience other symptoms of
overtraining as well. This may be especially problematic while on a caloric deficit.
Third, if you insist on doing something daily, you could take SC's advice and lift heavy 3 times a week and do cardio on the other days, or you could look into
crossfit. It's the workout routine of many military, police, firefighters, mixed martial artists, etc and is designed to develop general physical preparedness (ie, overall fitness). Rather than improving just strength or just endurance, Crossfit is designed to improve "each of 10 fitness domains: cardiovascular/respiratory endurance, stamina, strength, flexibility, power, speed, agility, balance, coordination, and accuracy." It does involve weight lifting, but also gymnastics, running, plyometrics, climbing and a whole lot more. The prescribed CF schedule is 3 on, 1 off, so you'd be working out 5-6 days per week. A few of these days would involve heavy lifting while the rest would be various metcon (metabolic conditioning) workouts that usually use much lighter weights or bodyweight.
Finally, no matter what routine you pick, if it involves an increase in intensity/volume, work your way up to it
gradually. Don't go from exercising 2-3 days per week to 6 days per week in one jump, or you body will not have enough time to adapt. This especially applies to CF where, even though the weights used are often light, the level of intensity tends to be incomparably higher than any other routine you've likely done. Scale the workouts, start with 1 on, 1 off and work your way up slowly from there.