TEL AVIV, Israel — Nearing the end of a whirlwind Mideast trip this week, Secretary of State Antony Blinken finished meetings with the Israeli president and relatives of American hostages held by Hamas, left his beachside hotel in Tel Aviv and shook hands with protesters gathered outside. He looked them in the eye and said there was a new hostages-for-cease-fire deal on the table that Hamas should take. Sign up for The Morning newsletter from the New York Times “Bringing your loved ones home is