The freak-out by the Israeli right, and supporters of the Israeli right, to President Obama's speech can be understood by Glenn Kessler's careful analysis explaining why Obama did break new ground. Previous administrations began from the premise that the 1967 borders had no validity and were militarily indefensible:

[U]ntil Obama on Thursday, U.S. presidents generally have steered clear of saying the negotiations should start on the 1967 lines. Here is a sampling of comments by presidents or their secretaries of state, with some explanation or commentary.
“It is clear, however, that a return to the situation of 4 June 1967 will not bring peace. There must be secure and there must be recognized borders.” — President Lyndon Johnson, September 1968
“In the pre-1967 borders, Israel was barely ten miles wide at  its  narrowest  point. The bulk of Israel’s population lived within artillery range of hostile armies. I am not about to ask Israel to live that way again.” — President Ronald Reagan, September 1, 1982
“Israel will never negotiate from or return to the 1967 borders.” — Secretary of State George Shultz, September 1988
Starting with President Lyndon Johnson, right after the Six-Day War, U.S. presidents often have shown great sympathy for Israel’s contention that the pre-1967 dividing line did not provide security.

Obama did not propose returning to those borders, but he uses them as a negotiating starting point. In that sense, Netanyahu and his supporters are correct.

Their error is in believing that this constitutes an important threat to Israel's security. During the first quarter-century of Israel's existence, the prospect of a massed conventional military invasion constituted the greatest threat to its existence. That's no longer true. The greatest dangers today are the combination of demographic and political threats posed by the growing relative size of the Arab population west of the Jordan river, terrorism, and the loss of legitimacy posed by a continuing occupation and counter-terrorism policy in the West Bank and Gaza. Those dangers all dwarf the potential that armored columns of Arab armies will cut Israel in half. The tragedy is that huge swaths of the Israeli right and its sympathizers (both Jewish and Gentile) have failed to grasp this, and have placed it in danger of succumbing to the mortal new threat while guarding against the antiquated one.