America has ~330 million people. Let's assume the 18.7 Million was just in the month of january..not 100% acurate, but not 100% inaccurate. That gives us a timeline of more than 1 year at current rate to vaccinate the entire US. Even vaccinating 70% the population will take roughly a year at current pace. Puts things in some perspective.
1. As time goes on, more staff is trained and protocols are learned. Bugs are ironed out. Vaccinating people becomes faster overall.
2. All the high-impact vaccinations are done at the beginning. By the end of January, most western countries will be done vaccinating their highest-risk groups. This is the highest impact of all the vaccination phases because the high-risk groups represent the highest amount of hospital cases, so this will greatly reduce load on hospitals, which in turn will reduce transmissions in hospitals and free up healthcare personnel, and so on.
3. More vaccines are still being approved. The Pfizer vaccine is the one that is most in use right now, and it has logistical complexity attached due to its storage requirements. With more vaccines in play, this will become less of an issue making distribution easier outside of cities especially, and speeding up vaccinations overall.
There's good reasons to be positive about the vaccines right now. I do wish my country (Belgium) would focus all its efforts on it, because our current vaccination logistics are pathetic.