The question is quite generic (no objectives on train or diet given). So, I'll answer based on my experience. When I want to cut (lose fat) I give a 3 week buffer period before changing the plan (diet or train) if not seeing the desired results.
For instance, you are aiming to lose 1 lb of weight per week. But, it is common for the weight to fluctuate (water retention, more food in your gut, ...). To minimize this, you should try to weight yourself always in the same conditions - fasted, first thing in the morning. Still, it happens quite frequently.
Consider the following weekly weight evolution:
- -3 lbs (nice! - but most part of it is just water and glycogen depletion...)
- -0.5 lbs
- -0.7 lbs
- -0.4 lbs
Looking at weeks 2, 3 and 4 you are clearly not losing an average of 1 lb per week. Now, after 3 weeks of not seeing the desired results, I usually do a slight adjustment - decreasing the calories by, for instance, 10% (cut on carbs and fats, maintain protein quantities high). This pretty much covers the diet part.
Now, adjusting the train routine is quite more complex. What I believe works best is continuing with your strength train (to retain as much muscle as possible) and do some [more] low intensity cardio in off days. The more cardio you do (let it be low intensity or it can tamper with recovery), the more calories you burn.
Problems? Well, most of the times when you go for a huge caloric deficit your lifts will suffer. Here, a more mild approach might be desirable according to your objectives (the urgency to lose fat and how much you value your muscle mass). Also, the leaner you are, the more strict you need to be (tighter diet and maybe more cardio depending on your genetics).