He cannot. The president can veto the bill, returning it to Congress without his signature. Congress can override the President's veto by a two-thirds vote of both the House and the Senate. If the Congress overrides the President's veto, it becomes law even if he doesn't like it.
If the President refuses to enforce the law, he is violating his Constitutional oath to ensure that the laws will be faithfully executed, which would be an impeachable offense. Congress could then "fire" the President by removing him from office.
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A president can veto a bill that the congress passes and sends to him for his signature and he can refuse to sign it (vetoing it). But the president cannot override vetos. The congress can override president's veto by a 2/3 vote.
If the president vetoes a bill, then Congress can override that vetoe, but the bill must go back to Congress to be approved with a majority vote.
2/3rds of congress must vote to override
The bill that the President has vetoed must be passed with a 2/3 favorable vote in both houses of Congress in order to become law.
A congressional override means that a bill has become a law even if the President refuses to sign it. The Congress can override it with two-thirds vote with both houses voting separately.