The Republican Party had control of the Presidency, the Senate, and the House of Representatives, but were held hostage by the Democrats. Now the Democrats have the House and everyone acts like they have control of Washington and the Republicans act like their power is gone. How can this be?
All legislation in Washington is subject to four-way negotiations: The House, the Senate majority party, the Senate minority party, and the President. This is because a simple majority is needed in the House, but 60 votes are needed to pass anything controversial in the Senate (barring the "nuclear option", which has been applied to judge confirmations, and a few other exceptions).
So the House only has one party that matters: Assuming all bills are subject to a party-line vote, the party that controls the majority in the House can pass anything they want, and the minority party can't do anything. (In real life, this gets more complicated when some members of a party say they won't vote for something without changes, and there may be crossover voters, etc.)
In the Senate, the minority party also matters, unless the majority has 60+ seats. That's because they can filibuster legislation they don't like, until the Senate leadership withdraws it. If a party has 60+ seats, then it's the only one that matters, but anything between 50 and 60 seats will require some amount of negotiation to pass anything.
Finally, the President has to actually sign anything that gets past both chambers - if he vetoes it, it's still dead. Thus even if one party had total control of both, if the White House was held by the other party, then there's still compromise involved. That is, unless the majority party has 2/3 of the seats in both chambers (292 in the House, 67 in the Senate), in which case they can override a veto and push through anything they want.
- Senate majority has 50-59 seats: Four way negotiations. (This is the category that both the previous Congress and the current one fall into)
- Senate majority has 60+ seats: Three way negotiations.
- Senate majority has 67+ seats and House majority has 292+ seats: Two way negotiations.
Because when they say who controls the senate they don't take into account the filibuster which needs 60 votes to break instead of the normal 50% + 1 votes. Until the new session started the Republicans had the ability to pass a bill in the House and Senate without a single vote from a Democrat (that is ignoring the filibuster) and get is signed by the president.
It can also be said that they are in control because they had the ability to decide everything that would come in front of both sides of congress and because of that which would get a chance to be put in front of the president.
Also just because they are said to be in control doesn't mean that they still won't need to work with other parties (the Democrats in this case) to get work done.