Part of the reason, of course, is that he is from the Likud party. Likud is seen as the Israeli equivalent of the Republican Party by many American liberals. That is an oversimplification and is really incorrect. The Prime Minister himself corrects journalists, steadfastly referring to Likud as center-right. Israel is a multi-party system and, much unlike the Republicans, those right of center divide into a number of secular and religious parties. Prime Minister Netanyahu has committed himself to "two states for two peoples" and he is the elected leader of Likud. That position is an anathema to the truly right-wing parties, for example, National Union, which is in opposition to the current government.
This Prime Minister lost his government during his previous term when the right wing parties pulled out of the ruling coalition, including breakaway members of Likud. It wasn't the left that brought him down; it was the right. Why? He signed the Wye River Memorandum and gave control of more land to the Palestinian Authority, including most of Hebron. I have no doubt that Prime Minister Netanyahu would do the same again if there was a real chance for peace. Right now there isn't one.
The problem is, and always has been, the Palestinian leadership. They have had a total of three leaders since 1919: Haj Amin al-Husseini, who sided with the Nazis in World War II and wanted to bring Hitler's final solution to Palestine, his nephew and chosen successor, Yassir Arafat, and Arafat's hand-picked successor, Mahmoud Abbas, whose doctoral dissertation amounted to Holocaust denial. Yes, people can overcome their past. Anwar Sadat flew planes for the Nazis and led Egypt to war on Yom Kippur in 1973. Today we remember Sadat as a man who gave his life for the sake of peace. Sadly, Abbas is no Sadat. He insists on terms that he knows Israel can never meet as preconditions to negotiation, guaranteeing their failure in advance.
Look what Prime Minister Ehud Olmert offered the Palestinians in 2008: land equal in area to what Jordan and Egypt occupied prior to 1967 with land swaps to account for present demographics, a divided Jerusalem with holy sites under international control, and a symbolic, limited acceptance of some Palestinian "refugees" into Israel. It's the most Israel probably could ever offer. The Palestinians didn't even respond and offered no counter-proposal.
What on earth could Prime Minister Netanyahu offer that hasn't already been offered? How is Prime Minister Netanyahu an obstacle to peace when he repeatedly says he will negotiate at any time in any place the Palestinians may choose? He's made the same offer to Syria. The answer is simple: Prime Minister Netanyahu is not a problem except in the minds of those who always find reason to blame Israel and those who believe them.
