Washington and Paris had been expected to circulate a new draft of the resolution on Monday but decided to wait to hear from the Arab delegation on Tuesday afternoon.
If a new draft was circulated late Tuesday, the earliest a vote could take place would be Wednesday - and some diplomats were guessing it would be put off until Thursday.
Tarek Mitri, sent to the UN as a special envoy by Lebanon's Council of Ministers, criticized the resolution's failure to demand an Israeli pullout and its call for Israel to halt only offensive military operations, which he called "a recipe for the continuation of violence."
Hizbullah has said it will reject any halt in fighting that leaves Israeli troops in Lebanon, and Israel has insisted it won't withdraw until it is guaranteed Hizbullah rocket fire will stop.
Mitri also criticized the resolution's failure to give Lebanon's year-old democratic government enough political clout to stand strongly against Hizbillah and to adequately address the issues of the disputed Chebaa Farms area on the Lebanon-Syria-Israeli border and Lebanese detainees in Israel.
"If they think by just adopting willy nilly a text like this one they would have done good, we would like to tell them that this is not so," Mitri said in an interview.
"I want a text that will bring about cessation of hostilities," he said. "We don't want a piece of paper that calls for cessation of hostilities while hostilities are exacerbated, aggravated, continue unabated."
France's UN Ambassador Jean-Marc de La Sabliere and US Ambassador John Bolton negotiated the text and kept Israel and Lebanon informed. Mitri said that when they were putting together the final draft, Lebanon warned the French that it was not acceptable.
De La Sabliere insisted the draft "is a good one" because it addresses the cessation of hostilities and sets out principles for a long-term solution.
"And I am going to work today to improve the text," he said. "We have to take into account the concerns of all and this is what we wish to do."
De La Sabliere noted that it was the Arab League just a little over two weeks ago that asked the Security Council to act - and he wants to hear from their representatives.
"We're still working on things," Bolton said. "Obviously we want to hear from the Arab League ... and then we'll decide where to go from there. ... We've said from the get-go that we want this to be in the context of a sustainable long-term solution. That's still what we're trying to work out."
Since September 2004, the Security Council has been urging the Lebanese government to extend its authority throughout the south, which remains under Hizbullah control, and to disarm the Islamic militia, which has demonstrated its military prowess during the current conflict.
Mitri said the 40,000-strong Lebanese army has not been able to extend its authority in south for political reasons but he said "now the political conditions are there for us to deploy the army" and the government is prepared to send as many soldiers as needed.
On Sunday, Justice Minister Haim Ramon said the US-French draft was good for Israel - but the country still had military goals and would continue its attacks on Hizbullah. Ramon also expressed doubt that Hezbollah would honor the resolution and stop firing.