I assume that whoever wrote this for Occupy Democrats is a natural born citizen, and did not have the same benefit of studying the constitution for the citizenship exam that naturalized citizens like me have had. Let me quote from Article III, section 3:
Treason against the United States, shall consist only in levying War against them, or in adhering to their Enemies, giving them Aid and Comfort. No Person shall be convicted of Treason unless on the Testimony of two Witnesses to the same overt Act, or on Confession in open Court.
One could argue that by disrespecting the president in war time people are providing aid to the enemy. However, that is a pretty tenuous argument, especially when it involves a president’s domestic agenda. Historically speaking, the US has allowed pretty strong criticisms of its presidents. Historically, there has been a crime that involved disrespecting your country’s ruler. It was called lèse majesté, or injured majesty. As the name suggests, it is appropriate where the ruler of the country is a sovereign king, not in a republic where the president is merely an employee of the body of citizens. A law similar to lèse majesté would be unconstitutional in the US, because of the First Amendment:
Congress shall make no law … abridging the freedom of speech, or of the press …