How does the president exercise legislative power over Congess?

Answer 1

The President has no legislative power "over" Congress (though s/he has one "of" Congress... more on that near the end of this answer). That said, the president has a sort of conditional legislative power over Congress. It's called "the presidential power of veto." This answer will cover a couple other presidential powers which, at least in the short-term, are sort of powers "over" Congress; but, really, in the long-term, they're not.

After both houses of Congress (the House of Representatives, and the US Senate) pass a bill intended to become law, said passed bill is the given to the president to sign. The President then has ten (10) days to either sign it or not sign it, and then, in either case, return the bill to Congress. That's the deadline: 10 days.

If the president signs the bill within ten days, and returns it to Congress; and if Congress is still in session when he does, then the bill becomes law. If the President does nothing -- in other words, if he both doesn't sign the bill, and also doesn't return it to Congress within the ten-day deadline -- and if Congress is still in session at the end of said deadline, then the bill becomes law, even without the President's signature.

However, if the President decides he doesn't like the bill, then he can "veto" it. The word "veto" is Latin for the phrase "I forbid." There are two ways the President may veto... only one of which ensures that the bill won't become law.

If the President refuses to sign the bill, and timely returns it to Congress, unsigned, within 10 days; and if Congress is still in session when he so does, then the President has vetoed the bill, and has stopped it from becoming law...

...but only if Congress decides to accept that from the President and do nothing further. The veto is the President's way of sending a very serious message to Congress telling it that he does not want the bill to become law. In order to ensure that Congress takes that message seriously, the Constitution requires that if Congress wants the bill to become law then it must re-vote on the bill...

...but this time, on that re-vote, Congress must pass the bill by a whopping two-thirds majority. That means that 66% of Congress must all agree that it so wants the bill to become law that it's willing to override the President's veto and make the bill law, even without the President's signature. The Constitution says that Congress's so doing requires a two-thirds majority re-vote on the bill. If Congress does that, then the bill becomes law right then and there, without having to be re-submitted to the President for his signature. Congress, at that point, has overridden the President's veto.

There is, however, a way for the President to veto a bill which will ensure that it won't become law, no matter what. Timing, however, is key to the President's being able to do that; and it can only happen under a very special circumstance, to wit: If Congress submits a bill to the President for his/her signature; and if Congress will no longer be in session by the time the 10-day deadline for the bill's return expires, then all the President has to do to effectively veto the bill is absolutely nothing. By his/her neither signing it, nor not signing it; but, in either case, his/her not returning it to Congress at all; and by Congress's adjourning before the President's 10-day deadline to return the bill either signed or unsigned, the President has effectively vetoed the bill; and because Congress is no longer in session at the end of the 10-day deadline, it may do nothing about the veto. And so, then, the veto really and truly stops the bill from becoming law. That kind of veto is called a "pocket veto." To keep it from happening, most sessions of Congress will never submit a bill to the President for his/her signature within the last 10 days of said session, that is, unless Congress knows, for sure, that the President will quickly sign and return it, before the session ends.

In a sense, then, that's the President's "legislative power" over Congress: the power of veto. But that power is conditional; and only works, absolutely, in the case of a pocket veto. At all other times, if Congress doesn't like the president's veto, then it can override it by a two-thirds majority re-vote, and make the bill law, anyway!

The President also has the power to introduce his/her own bills into Congress, on which Congress must take action, exactly the same as if Congress, itself, had introduced the bill. But that's more a presidential power of Congress, not over it.

The President also has the power, "on extraordinary occasions," according to the Constitution, to call Congress -- either or both houses of it -- into "special session," during periods when Congress is normally in recess, in order to handle emergency situations. That presidential power rarely used, though: the last time was back when Harry Truman was president, in 1948. In all, throughout the entire two-and-a-quarter centuries that there have been US presidents, the presidential power of calling Congress into special session has been used only 27 times (at least as of this writing in April of 2013). And so, then, that presidental power over Congress -- if, indeed, that's what it even is -- is nearly never actually used by most presidents.

Answer 2

Recommending Legislation.

See, also, the "related questions" section, below, for a link to a considerably expanded answer.

Answer 3

the president