For many people, "feel like" has become a complex verb that takes sentential complements:
(link) I feel like that I am neglecting my diary.
(link) Within weeks you will notice dramatic changes in your energy levels, and in about 3 months you will feel like that you are a completely different person.
(link) But my problem is that when we talk on the phone he is not much interested in talking and I feel like that he is not interested in me anymore but when I see him he is more passionate than before.
(link) Her and the owner are very close and I feel like that she is telling the owner not to give me the full responsibilities of being a manager because she feels threatened by me.
(link) We feel like that we're making a lot of progress, but a few things cause us to be of continuing concern.
(link) I feel like that they really should have should have taken care of their promise.
(link) I was wondering if you feel like that the Peninsular War is your turf?
(link) Do you feel like that a woman can handle this job?
Apparently phrases such as "I feel like a truck ran over me" are analyzed as analogous to "I believe a truck ran over me", and thus it is felt that a missing that can be supplied in both cases.
The same thing seems to have happened in these examples -- along with some other re-analysis or blending in the cases with referential subjects:
(link) It seems like that you discovered yourself when you found the writer Lorenzo in the story.
(link) The few times that Dantzler was sacked or stopped by the defensive line, it seemed like that they would gain it all back and then some with the next down.
(link) He seems like that he could care less if it is anything worse.
(link) Every time she sees me, she seems like that she wants to kill me.
(link) It's hard to believe that the live tracks were improvised, as they seem like that they had have been composed.
(link) It looks like that I'll be arriving there in the middle of June.
(link) I like him coz he looks like that he is always thinking about something.
(link) i think that she is really pretty!!! but in the first one she looks like that she smoked a pack of cigarets in 5 minutes and cant breath.
[Update: this is apparently not a new development. In a letter from S. Randolph Adkins to his aunt Sarah Adaline Thorne Merritt, datelined Petersburg, Va. July 6, 1864, he complains that "I have not herd from you nor the peeple of that neighborhood in sum time it appears like the peele has all quite riting and has all forgottten the soldiers that is far from home and friends", and points out that:
it dus not appear like that it would be a very difacult matter to rite a fw lines to a friend at a lesure time
]
Posted by Mark Liberman at June 17, 2004 10:30 AM