There is the potential to incur quite hefty fines, penalties or even imprisonment – but that depends on several circumstances, like intent etc. These laws were enacted because of the symbolim attached to the bird.
As can be read on the Wikipedia page, the bald eagle was considered endangered as a species, primarily by DDT and then shootings.
On killing the bird now, the US Fish & Wildlife Service lists the following:
Federal Laws that Protect Bald Eagles
Bald and Golden Eagle Protection Act
The bald eagle will continue to be protected by the Bald and Golden Eagle Protection Act even though it has been delisted under the Endangered Species Act. This law, originally passed in 1940, provides for the protection of the bald eagle and the golden eagle (as amended in 1962) by prohibiting the take, possession, sale, purchase, barter, offer to sell, purchase or barter, transport, export or import, of any bald or golden eagle, alive or dead, including any part, nest, or egg, unless allowed by permit Bald Eagle sitting in tree (16 U.S.C. 668(a); 50 CFR 22). "Take" includes pursue, shoot, shoot at, poison, wound, kill, capture, trap, collect, molest or disturb (16 U.S.C. 668c; 50 CFR 22.3). The 1972 amendments increased civil penalties for violating provisions of the Act to a maximum fine of $5,000 or one year imprisonment with $10,000 or not more than two years in prison for a second conviction. Felony convictions carry a maximum fine of $250,000 or two years of imprisonment. The fine doubles for an organization. Rewards are provided for information leading to arrest and conviction for violation of the Act.
**Migratory Bird Treaty Act
The Migratory Bird Treaty Act is a Federal law that carries out the United States’ commitment to four international conventions with Canada, Japan, Mexico and Russia. Those conventions protect birds that migrate across international borders.
The take of all migratory birds, including bald eagles, is governed by the Migratory Birds Treaty Act’s regulations. The Migratory Bird Treaty Act (MBTA) prohibits the taking, killing, possession, transportation, and importation of migratory birds, their eggs, parts, and nests except as authorized under a valid permit (50 CFR 21.11). Additionally, the MBTA authorizes and directs the Secretary of the Interior to determine if, and by what means, the take of migratory birds should be allowed and to adopt suitable regulations permitting and governing take (for example, hunting seasons for ducks and geese).
Penalties under the MBTA include a maximum of two years imprisonment and $250,000 fine for a felony conviction and six months imprisonment or $5,000 fine for a misdemenor conviction. Fines double if the violator is an organization rather than an individual.
The MBTA and its implementing regulations provide authority for the conservation of bald eagles and protect against take if the Endangered Species Act protections are removed.
The Lacy Act was passed in 1900, and protects bald eagles by making it a Federal offense to take, possess, transport, sell, import, or export their nests, eggs and parts that are taken in violation of any state, tribal or U.S. law. It also prohibits false records, labels, or identification of wildlife shipped, prohibits importation of injurious species and prohibits shipment of fish or wildlife in an inhumane manner. Penalties include a maximum of five years and $250,000 fine for felony convictions and a maximum $10,000 fine for civil violations and $250 for marking violations. Fines double for organizations. Rewards are provided for information leading to arrest and conviction. violation of the Act. For more information on the Lacey Act
The hefty penalty for organisations is a difficult point, though, as it includes wind power operators.
New Wind Energy Permits Would Raise Kill Limit of Bald Eagles But Still Boost Conservation, Officials Say
The U.S. Fish and Wildlife Service proposed a new plan today that would allow energy companies to operate with permits lasting up to 30 years, while also raising the number of bald eagles they can kill or injure per year without incurring hefty penalties to 4,200, which is nearly four times the current limit.
And it is sometimes quite a difficult dance on the lines of the law. For farmers:
When the National Bird Is a Burden
The eagles were killing thousands of his chickens. How many exactly? That was unclear. He knew he needed to stop it, but what do you do about a bald-eagle infestation? Nobody in Bluffton had ever heard of such a thing.
Harris is an idealist, the kind of all-natural farmer whose cows finish on grass, whose birds run free, whose goats and sheep transform overgrown land. His faith in biodiverse, sustainable methods has only been affirmed by his multimillion-dollar annual revenues. And not that he would, but shooting a bald eagle is punishable by a $100,000 fine and a year in prison.
Why were these laws enacted?
Rebecca F. Wisch: "Detailed Discussion of the Bald and Golden Eagle Protection Act", Animal Law Legal and Historical Center, 2002
In 1940, Congress recognized the need to protect the Nation’s symbol of freedom and liberty. The Bald and Golden Eagle Protection Act was originally borne of a need to protect only the bald eagle. Faced with population pressures due to direct hunting and habitat encroachment, Congress enacted protection for this majestic bird of prey. The Eagle Act, as originally enacted, prohibited any form of hunting, possession, or sale of the bald eagle. The Act protected both live and dead eagles covered by the act, as well as eagle parts, nests, and eggs. Later amendments increased the penalties proscribed by the statute, which include civil and criminal sanctions.
In 1940, Congress acted to prevent what seemed to be the inevitable destruction of the Nation’s symbol. The purpose behind the enactment of the 1940 version of the Bald Eagle Act, as it was then known, can be explained through the words from the Acting Secretary of Agriculture in 1939:
It is apparent to this Department from its long observations with respect to the wildlife of this country that there are those in any community in which an eagle may appear who are immediately seized with a determination to kill it for no other reason than that it is an eagle and a bird of large proportions. It is equally apparent that if the destruction of the eagle and its eggs continues as in the past this bird will wholly disappear from much the larger part of its former range and eventually will become extinct.
From an esthetic point of view there can be no question as to the desirability of protecting the eagle. Its status as the emblem of the sovereignty of the United States settles that; the bird should be a ward of the National Government . Real lovers of nature, of which there are millions in this country now, count it a red-letter day when they see an eagle, and they are united in support of legislation such as is proposed in this bill. They would regret beyond expression to see the now evident process of extinction of this bird continue and fervently hope that it can be checked for all time by the Congress of the United States.
So it seems pretty sad that the US did not adopt much much more species as a national symbol.