Should Israel Shift Strategies from Attack to Siege?

At 2:30 AM on Thursday, local time, Hamas informed the mediators in the hostage negotiations (most likely Egyptian and Qatari diplomats) that it rejected Israel’s most recent proposal to pause the fighting and release Palestinian prisoners (probably in the hundreds) in exchange for about half of the living hostages. Later that day, both Washington and Jerusalem recalled their negotiators from Qatar. Steve Witkoff, the lead American negotiator, announced that he believes Hamas is not “operating in good faith” and that the U.S. “will now consider alternative options to bring the hostages home.” His statement raises several questions, most importantly: why did he ever think Hamas was negotiating in good faith? And what exactly are those alternative methods?