to run for office - to try to be elected to a particular office (political position)
E.g. Will President Obama run for office again in 2016? No, he cannot, he would have served two terms already.
John has always been interested in politics and now he decided to run for mayor.
to throw in the towel - to give up, to admit defeat
E.g. He knew he was going to lose, so he threw in the towel.
Jimmy will never throw in the towel, he is a fighter.
common denominator - traits or characteristics certain people have in common
E.g. Lowering taxes seem to be the common denominator in today's politicians.
Mr. Brown likes political dinners. Food is often a common denominator among opponents, it has the ability to bring people together to have a balanced discussion about controversial topics.
to enter the home stretch - to get close to the end of the race
E.g. The political campaign is in the home stretch. The candidates are looking forward to getting the results next week.
"Let's give it everything we have got, we are in the home stretch now!"
mudslinging - destroy their opponent's good name by saying bad things or through misleading advertisements
E.g. I don't like the negative campaigning, this mudslinging is really annoying, it makes us dislike all the candidates.
The mudslinging did not help expand the media coverage of the issues, they have to find different tactics to succeed.
landslide victory/by a landslide - a victory when one candidate receives an overwhelming majority of the votes
E.g. In the 1997 General Election, Tony Blair and his Labor party had a landslide victory.
Their coalition was re-elected by a landslide.
neck and neck - very close in a race
E.g. The opponents were neck and neck in the race for office. Their votes were tied.
The opinion polls showed the two candidates are running neck to neck.