No way to solve the problem. You can't make the file have more information than it has.
You can try to work around the issue. Couldn't you try to make say vlc work in full-screen on TV? I don't know how your TV is set up, but it should be enough to just drag the VLC window over to the TV and play the movie, right click on the video and select video->full screen.
It should scale the video across the TV's screen. There will be degradation of quality, but it should be full screen.
Your source material is encoded with lossy compression. To maintain the video quality after editing, the video would have to be exported with lossless compression, which is far less efficient and thus results in a larger file size.
The alternative is to re-encode the material with a lossy algorithm, but even if you mimic the compression settings of the original clips, the quality will suffer. This is called 'generation loss'. Wikipedia has a nice visual example pertaining to re-encoding JPEG images a large number of times. You can of course export the video with an arbitrary compression algorithm to reduce the quality degradation at the cost of a larger file or vice versa.
If you are simply merging two clips, similarly encoded and to be played in succession, into one file, and doing no other editing, it may be possible to create the new file without re-encoding, but by joining raw file contents and manipulating them into a valid .mp4. I suspect Final Cut Pro cannot do this, but there may be tools that can, such as YAMB.
Best Answer
Yes there is. To bring up the tool that is built into Expression, go to Window and click on "Summary" to check it.
You can also estimate it yourself using one of the formulae you can read about here: http://forum.videohelp.com/threads/299571-How-to-calculate-size-of-video-file-after-encoding