Some have questioned whether the resolution is even legal, and others said they want a response to Khashoggi's death but agree with the Trump administration that Washington should continue to back the Saudis as an essential counterweight to Iran.
Bin Salman has denied any knowledge of the plot to torture, murder and dismember Khashoggi at the Saudi Consulate in Turkey in October and the USA has waffled on whether it believes his denials.
That was referring to the culpability of Saudi Crown Prince Mohammed bin Salman in the murder, which took place inside the Saudi consulate in Istanbul.
The UN High Commissioner for Human Rights Michelle Bachelet yesterday called for an worldwide investigation.
Initially, Saudi authorities had said Khashoggi, who had written articles critical of the crown prince's policies, had disappeared, after safely leaving the consulate.
"It's really unsafe for America to look away here", Graham said.
"The worldwide community seems to doubt Saudi Arabia's commitment to prosecute this heinous crime", the official continued.
The senator said he could not support Saudi Arabia's involvement in the war in Yemen or arms sales to the Saudi government as long as the crown prince remained in power.
Saudi Arabia has said the crown prince had no prior knowledge of the murder.
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Corker said Thursday that senators are looking at moving three measures - a resolution to condemn the crown prince for Khashoggi's murder, a bill to suspend arms sales to the kingdom and a resolution to call on President Donald Trump's administration to pull back US help for the Saudi-led war in Yemen.
The measure also cites the initial insistence from Saudi officials that Khashoggi had left the consulate unharmed - statements that proved to be false.
Turkey has been seeking to extradite 18 suspects, including 15 members of the alleged assassination squad.
The administration last week sent Mattis and Pompeo to the Capitol, but senators emerged angrier than before, in part because Haspel didn't participate.
Senate Foreign Relations Chairman Bob Corker told Roll Call Tuesday afternoon that interested parties would be meeting on Wednesday to try to find an agreement on handling the contentious Yemen resolution.
Sen. Rand Paul, meanwhile, went to Twitter to voice his opinion, smashing the caps lock to say "ENOUGH!" in regards to Saudi Arabia's behavior.
"It's not a smoking gun".
Menendez has called for a strong United States reaction to Khashoggi's death and backs legislation to end all United States support for the Saudi coalition waging war in Yemen. If he was in front of a jury he would be convicted in 30 minutes.
"I think it would have been good to have the full Senate", said Sen. "It's not based on friendship as much as it's based on common interests, combating extremism in the Middle East and countering the Iranian threat", said Senator John Cornyn, the chamber's No. 2 Republican.
"They're clearly valuing business over human life", Shireen al-Adeimi, a Yemeni-born assistant professor of education at Michigan State University, said.