Well, typically the winning candidate has the unified support of their party. So, if a Republican president wins, and Republicans control Congress, then the president basically has the support of Congress. It gets a little trickier when the opposing party controls Congress because then you have a divided government. Some people prefer a divided government because they believe the controlling opposition provides a check on the power of the president. Others are opposed to divided government because it makes executing the president's agenda more difficult, which is either good or bad depending on whether your party is in control of Congress.  

 Yep. But if you have 40% of Congress, you can get things done with a little negotiations. If you've 0% you're getting nothing done.  

 That's true. Although it depends on how willing members of the other side are to negotiate, and work across the aisle. In a perfect world, our elected leaders would prioritize getting things done for the American people over the tribal partisanship. But as has become apparent, we definitely do not live in a perfect world.  

 3rd parties absolutely need to build their support and infrastructure through local and state elections before they can expect to be able to compete, and be a viable choice.