The Republican party is the party that is threatening to split and if it did the remnants would have the best shot at appealing to the blue dogs IMO.
The threat to entitlements is coming from the financial reality of entitlements not the political reality. Politicians would like to just ignore them but that is becoming increasingly difficult.
A third party in the US is unlikely no matter what but IMO the most likely scenario is the one I described.
The moderate Republicans are not willing to forfeit the GOP to the extreme right just yet. They will fight tooth and nail for control and that battle will take place this year. I fully expect the TP'ers to cost many moderates their seats by defeating them in the primaries however there will be a cost associated with this and it will be smaller representation overall in the House. Dividing the party will leave open opportunities for Independent and moderate Dems to take seats where the electorate is not happy about the gridlock and obstruction of the extreme right.
Given that scenario there is no reason to believe that blue dog Dems will join the GOP. Historically "party swappers" always move towards power rather than away from it. The power trend is towards the Dems according to the demographics.
The "threat to entitlements" stems primarily from the extreme right. They will need to prevail overwhelmingly in the elections this year in order to make that threat into reality. That means winning 6 Senate seats and losing none at all. Assuming they reach that goal they still won't be able to override a presidential veto because that would mean winning 16 seats without losing any. That is about as likely to happen as winning the Powerball lottery.
So your scenario is based upon an assumption that is unlikely to occur in my opinion. The most likely outcome is that the status quo remains essentially the same as it is now in 2015 give or take a couple of seats here and there. The problem the extreme right has is that it doesn't have any more "political weapons" that it can throw at entitlements. Shutting down the government and refusing to raise the debt ceiling are both discredited and they have cost the GOP dearly so they won't be able to use them again for at least another decade.
All that leaves is good old horse trading and with neophyte TP'ers up against seasoned Dems the outcomes are going to be superficial "victories" without any real substance.
There are a lot of moderate to right leaning voters in this country. The TP platform will continue to attack moderate Republicans in primaries in heavily Republican districts. This will open the door for right or moderate leaning Dems to attract the Republicans who are not as extreme as the TP.
Moderates and the middle class have been ignored by both parties to the detriment of the nation. It is just a matter of time before they start fighting back.
Entitlements are a financial problem. There is really no point in denying that.
The "libertarian" arm of the Republican party has plenty of money and power to remain in power.
The only real hope the nation has for a third party is a moderate party.
Authoritarian corporatists unite!