In the united states, what check does the president have on the power of the legislative branch?

He can either veto a law or cancel anything in his/her way.  The president’s veto can also only be overridden by a two/thirds majority vote in both the House and the Senate. 

While the president often plays a role in crafting legislation, it is up to Congress to vote on and pass it. However, the president can veto any piece of legislation. This veto power is limited because a two-thirds majority vote in both the House and the Senate will override the veto and make the legislation law.