Can the President give the V.P. the reigns to carry out Presidential duties and work as his direct second in command?
The Constitution gives the vice president the role of presiding over the Senate, and voting in the Senate if there is a tie. The vice president's only other formal responsibility is taking over the presidency if the president dies.
Essentially, that's it.
After that, if the President confers authority to the VP to act in his/her name then that's OK...but the responsibility still lies with the President for any actions & outcomes.
You might try this question at Politics.SE for a more informed answer/debate but this summarises it....
The President is free to delegate tasks as much as he would like. There is no barrier to that. However, the President cannot delegate Constitutional or statutory authority or the implied responsibility of the President. That always resides with him. For example, the President remains the Commander in Chief.
Q & A at Politics.SE
Has this happened before? As far as I know the Chief of Staff is in the need to know more than the V.P. sometimes.
Not to the extent we see in this fictional TV show given that the Underwoods are a married power couple working hand in hand for joint (mostly) purposes but...
Historically, the vice president's level of government involvement has varied. More recently, second-in-commands have taken a more hands-on role, Brace said, with Al Gore, and perhaps Cheney, being some of the most active.
John Nance Gardner, Franklin D. Roosevelt's VP, was one of the least involved, and famously said the vice presidency wasn't worth "a warm bucket of spit." (Reporters allegedly changed the spelling of the last word for print).