The separation of powers has come into play during the Obama administration, as it has during every other administration. Yesterday, the president said of immigration reform:
Now, of course, there will be rigorous debate about many of the details, and every stakeholder should engage in real give and take in the process. But it’s important for us to recognize that the foundation for bipartisan action is already in place. And if Congress is unable to move forward in a timely fashion, I will send up a bill based on my proposal and insist that they vote on it right away.
The president's formal authority in this respect is limited. Article II, section 3 of the Constitution says: "He shall from time to time give to the Congress Information on the State of the Union, and recommend to their Consideration such Measures as he shall judge necessary and expedient." The president cannot directly introduce legislation, and has no constitutional power to compel any particular action.
The first step in the legislative process is the introduction of a bill to Congress. Anyone can write it, but only members of Congress can introduce legislation. Some important bills are traditionally introduced at the request of the President, such as the annual federal budget. During the legislative process, however, the initial bill can undergo drastic changes.