Beirut's airport was closed after Israel warplanes bombed its runways, and every night is punctuated by the sound of airstrikes.
"I have two kids [and] a baby, and they're scared. I'm scared," Esseily said. "First time I've ever encountered something like this."
The Esseilys are among tens of thousands of Westerners stranded in Lebanon Tuesday waiting for help to arrive. Monika Esseily said she's in contact with many other Americans in Lebanon and that all of them want to get out.
"They're pulling out their hair, they're crying, they're saying 'What's going on?' They're being rejected from the American Embassy," she said. "The American Embassy is still saying, 'We will call you.' That's all that they will say."
Some Europeans and Americans have piled on to cruise ships to flee the country.
The United States expects to evacuate more than 2,400 Americans from Lebanon by Thursday, most of them aboard two chartered ships, State Department and Pentagon officials said Tuesday.
The Esseily family registered Thursday with the American Embassy to get on the list to evacuate but so far haven't heard anything, she said.
"I just would love them to contact the Americans and say ... 'Hey, we know you're here, and we'll protect you, and we'll get you out.' Even if we have to pay, I don't care... They need to contact us," she said.
Nicholas Burns, the U.S. undersecretary of state for political affairs, defended the evacuation so far as "very well thought out."
"We have an open line to all American citizens. We're in touch with them by Web site. Those Americans who wish to leave will obviously go out," he told CNN Tuesday.
About 350 of the estimated 25,000 American citizens in Lebanon had been flown to Cyprus from the U.S. Embassy in Beirut by nightfall Tuesday, Maura Harty, the assistant secretary of state for consular affairs, told reporters.
