The Declaration of Independence doesn't apply to governments outside of our own. That document, along with the constitution, etc define the legitimate government of the United States.
The Declaration of Independence sets forth our grievances with the King of England, our fundamental beliefs about natural law and why we were justified in severing ties with the King of England. It does not define our government or form our government.
I would assume all Americans support the ideas set forth in the Declaration of Independence. One of those ideas is that a tyrant does not have legal authority.
This is the beginning of the Declaration of Independence:
When in the Course of human events, it becomes necessary for one people to dissolve the political bands which have connected them with another, and to assume among the powers of the earth, the separate and equal station to which the Laws of Nature and of Nature's God entitle them, a decent respect to the opinions of mankind requires that they should declare the causes which impel them to the separation.
We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness.--That to secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed, --That whenever any Form of Government becomes destructive of these ends, it is the Right of the People to alter or to abolish it, and to institute new Government, laying its foundation on such principles and organizing its powers in such form, as to them shall seem most likely to effect their Safety and Happiness. Prudence, indeed, will dictate that Governments long established should not be changed for light and transient causes; and accordingly all experience hath shewn, that mankind are more disposed to suffer, while evils are sufferable, than to right themselves by abolishing the forms to which they are accustomed. But when a long train of abuses and usurpations, pursuing invariably the same Object evinces a design to reduce them under absolute Despotism, it is their right, it is their duty, to throw off such Government, and to provide new Guards for their future security.--Such has been the patient sufferance of these Colonies; and such is now the necessity which constrains them to alter their former Systems of Government. The history of the present King of Great Britain is a history of repeated injuries and usurpations, all having in direct object the establishment of an absolute Tyranny over these States. To prove this, let Facts be submitted to a candid world.
So our most fundamental belief is that when a government become tyrannical it is no longer valid and the people have a right to remove that government or sever ties with that government. I referenced this because the existing Syrian government is tyrannical. It is therefore not legitimate. The people are in the process of over throwing it. They have internally declared it to no longer be the valid government.
For an American to say that government is legitimate just seems wrong to me. We of all people, should support at least with words, those that would rise up against tyranny for themselves and their future generations.
Apparently, you disagree and support the tyrant but my hope is you will actually rethink your position and conclude that the sitting government is not legitimate.