Making the request shouldn't create a bad impression-- managers that deal with employees that have family out of the country are generally accustomed to employees taking longer, less frequent vacations. As with any request, however, you need to be prepared to compromise or even have your request turned down. And you'll want to think through the concerns your manager and the company are likely to have.
If you are getting three weeks of vacation as a new graduate in the United States, for example, it is very likely that this is a combination of vacation time, sick leave, and other forms of paid time-off. If that's the case, your plans would require going two weeks negative in your accrued time off at the beginning of the year which would basically prevent you from taking a sick day for the first year of your employment. It's pretty unlikely that anyone can guarantee that you won't get sick for a year. That may make your manager concerned about when you would be able to get back to a 0 balance and whether that will involve you coming in to work when you're sick and infecting everyone else in the group.
The company may also have policies that prevent you from going too far into the negative on your accrued vacation. They may also have policies about how long a single vacation can be (and three weeks would likely be pushing the envelope). The company may be willing to let you go a day or two negative. But going two weeks negative may create issues for HR. If someone leaves the company with a huge negative balance, that almost certainly creates headaches for the company which is why they generally try to avoid the situation.
Is there something about this year that is particularly special? If there is a special reason that you want to be home this year, it may be easier for the company to deal with you having a one-time negative vacation balance. If your intention is to take a long vacation home every year, meaning that you would end up spending the first 8 months of every year getting back to a 0 balance, that is likely to be much more problematic. Companies are really wary of people that are continuously at a negative balance with no expectation that they'll ever be accruing their vacation time before they use it.
Depending on the type of job, there may also be political considerations. If, for example, your group is responsible for supporting a production process, it's likely that someone has to be working during the holidays to take care of issues as they come up. It so, it would be common for things like seniority to come into play where the more senior members of the group get the first choice of holidays and the newer employees have to work the days nobody else wants like Christmas or New Year's Day. There may also be projects that require work over the holiday period (the end of the year can be a popular time to install new software if that is a relatively slow period for the company. Or Christmas may be a key period for the company and they may want to minimize the time off people take in the lead-up to that holiday.