According to Bishop Williamson talks between the Church and the SSPX are to begin shortly. The matter for discussion will not be revealed publicly. It is sad that the Bishop sees the difficulties as irreconcilable. The following is from his blog.
The problem for these discussions is that, objectively speaking, as on either side there may be some reluctance to admit, we are in the presence of an irreconcilable clash between the religion of God and the religion of man. Vatican II mixed the two together, which was too much of the religion of man by half. Let us then say that Benedict XVI wishes to combine Vatican II with Catholic Tradition. That is still too much of the religion of man by a quarter. Let us now suppose that the SSPX and Benedict XVI were to agree to come half-way towards each other. That would still represent one eighth of the religion of man mixed with seven eighths of the religion of God, which for the purposes of Almighty God would still be one eighth too much.
For just as it takes a disproportionately small amount of water mixed with a tank full of gasoline (or petrol) to stop a car engine dead, so it takes only a small admixture of idolatry to stop dead the true religion of God. The Lord God Himself tells us that He is a jealous God (Exod. XX, 5; etc.), and will not endure any false gods beside Him. To anybody in the SSPX who might be tempted to worship with the neo-modernists, as to any neo-modernist who might wish to share worship with the Catholics, the Old Testament prophet Elias would say as he said to the hesitating Israelites, "How long do you halt between the two sides ? If the Lord be God, follow Him: but if Baal, then follow him." Scripture (III Kings, XVIII, 21) then says, "The people did not answer him a word".
Subjectively, the Israelites wanted to have it both ways. Objectively, that was impossible. For ourselves too. Kyrie Eleison.
I hope that the Bishop's pre-judgement on this is as faulty as are his judgements on other issues, as on other issues it might have been better if he he had kept silent.
However I suspect many of the SSPX are committed to Sede Vacantism and an irrevocable break with Peter in favour of an ethereal Rome of their own imagining. PRAY!