The main stumbling block is recognition of the State of Israel by ALL parties.

Israel's neighbours are:
Egypt - they have no problem in recognising the State of Israel;
Jordan - they likewise have no problem in recognising the State of Israel;
Syria - Still in dispute with Israel over land on the Golan Heights and over water issues. They sponsor terrorist organisations active in Israel, West Bank, Gaza and in Lebanon.
Lebanon - An artificially formed country carved out of the "old" Syria established in the dismemberment of the Ottoman Empire. Recently released from 27 years of Syrian occupation, but remains to be the main base for Hezbollah attacks on Israel.

Interested Parties:
Egypt - no problems, no particular axe to grind.
Jordan - no problems, no particular axe to grind.
Syria - Wants return of Golan and settlement of water rights
Lebanon - Wants settlement of land disputes with Syria and needs to evict Hezbollah to remove only point of friction with Israel.
Iraq - Non-frontline state, used to sponsor international terrorist organisations in the area targeting Israel, purely for inter-pan-Arabic political ends. Now no longer does so due to change of management.
Saudi Arabia - no problems, no particular axe to grind, wishes peace in the region.
Iran - Non-frontline state, main state sponsor of terrorist organisations in the middle-east, as formerly with iraq this is done for purely political reasons. Stated aim to "wipe Israel from the map". Possibly about to become a member of the nuclear weapons club.
Hezbollah - Political Party in Lebanon, currently attempting to overthrow the government there. An international terrorist organisation that targets Israel with the declared intent of total annihilation of the State of Israel.
Hamas - Current elected representatives of the Palestinian people. They have an internationally recognised terrorist wing responsible for indiscriminate attacks on Israeli civilians. Like Hezbllah, their stated aim is the total eradication of the State of Israel and its people.
Palestinian Liberation Organisation - Tosser Arafat's old crowd, they too have militants that call for the annihilation of Israel.
Palestinian Authority - Weak, corrupt, unable to govern this is the rump of the milch cow that Arafat fed from for decades in order to amass his personal fortune. His successors are reluctant to relinquish the spot as they too, no doubt want a similar sized slice of the pie. Unfortunately for them, the Palestinian people having grown tired of their conspicuous lack of leadership over the past three decades had the absolute nerve to elect Hamas representatives.

OK, irrespective of point of view, take the position of Israel, look at things from their perspective, under what basis would you enter into negotiations with the parties detailed above?

By the bye, 1948 boundaries are a "red herring", even according to those who wish to negotiate (This excludes, Iran, Hezbollah, Hamas, PLO/Fatah) the boundaries are those of pre-war 1967.