The next few verses after Matt 24:4 say this
4 And Jesus answered and said unto them, Take heed that no man deceive you. 5 For many shall come in my name, saying, I am Christ; and shall deceive many. 6 And ye shall hear of wars and rumours of wars: see that ye be not troubled: for all these things must come to pass, but the end is not yet.
The Great Tribulation period is 42 months or 3 1/2 years long. We could call the whole seven years period the tribulation I guess if we like, but not the Great Tribulation. The time of trouble with no historical comparison starts after the abomination of desolation is set up, midway through the seven years.
I see. So you would not include the last seven year period as the time of sorrows. Fair enough.
I do think that Israel will be the main focus after Christians are taken up. In Matt 24 it mentions
9 Then shall they deliver you up to be afflicted, and shall kill you: and ye shall be hated
of all nations for my name's sake.
The people He addresses here seem to be a nation!
Here you again seem to be calling the seven years the Great Tribulation.
I suspect you may be correct in the belief that the Rapture would be at the start of the seven-year period. I won't be dogmatic on that point though.
I do think that the old Roman Empire will form the crux of the final government also. It is possible you are correct and the US may be finished. However I suppose it might be possible it joins Europe as one of the kings, and is the 8th power, (yet of the seven). Who knows? So I don't want to step out on a limb and claim that the US has to be wiped out according to the bible, before the final seven years starts.
Basically, yes. It seems the real wicked couldn't care less what signs came, they will only blaspheme more.