Classifying objects based of a varying number of the same type of feature vector for each object
If I did not get you right please comment me. I would not go for doc2vec as you do not want to discriminate docs but persons. So better to concatenate speeches of each person to a single document and then feed it to word2vec/doc2vec (I assume you would like to use ANNs otherwise there are other options e.g. TF-IDF, etc.) In this manner each person will have a 300-d feature vector including a everything. (I would still try TF_IDF and CountVectorizer as well!)

If you insist on your current option, you may discard person info (you want to get a speech and say what kind of political-party the speaker is coming from, right?!) and set up your data as a 300-d feature vector for each speech whose tag is a political view (instead of taking mean of all speeches of 1 person). Then your feature vectors are all the same size (in this approach, each person might have several entry in the data which may bias the data so you may add a column including the speaker e.g. "speaker a", "speaker b", etc. Here you end up with a 301-d data).

Hope it helped. Good luck!