They can be completed without gems in the time given but to be honest, if you're a newer player that is still building up your in game resources then it'll be a while before you're at the point where you can complete all of the goals.
If you're further along in the game and have a large bank of coins then the key to 14 day goals is to build your appliances as quickly as possible which requires a LOT of coins so it's not always possible for newer players. Since we can only get 20 gifts and 20 requests each day most players use the "Dump Method" to gather as many collectibles as possible to build their appliances quickly. If you're unfamiliar with it, I explain the details of it here. Using the Dump Method, I usually end up wasting about $200,000 coins just to build my appliances quickly. I make the coins back within a day or two but still, it's a lot to essentially throw out.
I build 4 of the first oven and 5 of the second which normally lets me finish a few hours before the goal ends. Some players like to build even more than that but the perfect number of appliances will vary for each player. Once you figure out the perfect number of appliances for your playing style then it's just a matter of deciding if you've got the coins to waste to build them quickly via collectibles.
It used to be that once a goal was over we'd never see those items again so most players felt a real need to finish them. But now with the Echo Appliances and U-decos being released in sales it takes a bit of the pressure off - if players can't finish a goal they have the comfort of knowing they'll eventually see those items listed for sale in the future. It's not a perfect solution, but it is a lot better than it used to be and we can always hope it'll get even better as time goes on