In an effort to encourage the American citizenry to be more involved with its government, the White House set up an online platform for submitting petitions to the administration. If enough people sign a petition, the administration is obliged to respond to it. A petition posted in November quickly reached that number and now the White House has responded to the call to "Secure resources and funding, and begin construction of a Death Star by 2016."
The answer is no, even though such a program would spur job creation in many important fields and strengthen national defense. The official response explains its reasoning by pointing out that such a project would likely cost more than 850 quadrillion dollars ($850,000,000,000,000,000), the original design has a critical weakness that is easily exploited by one person, and "the administration does not support blowing up planets."
The response does go on to point out that there are many current and future programs to take us into a Star-Wars-like future, including programs at NASA and DARPA. If you want to read about them, follow the source link, but be warned, there are enough Star Wars references in it to choke a habogad.