This past week, California Senator Diane Feinstein said she believes that case contributed to Lam's downfall.
Intelligence Committee members received the same briefing given to the White House, Feinstein said.
Ms Feinstein said such exemptions would leave Americans with more than enough weapons to defend themselves.
"I think that the verdict is cast in terms of the votes, " Feinstein said.
Nevertheless, Feinstein said the issue was very important to her and she would not stop pursuing it.
Feinstein said she was "disappointed" with Reid's decision, which he told her about in a private meeting on Monday.
But Feinstein said she's hoping for resolution in the next day or two.
"The need to develop an overall cyber-security strategy is very clear, " Feinstein said.
"Today comes word of another tragic shooting at an American school, " Feinstein said.
"I met with my staff this afternoon, and nobody reported medical problems associated with anthrax, " Feinstein said in a statement.
"The theory is that private sector competition will drive down the cost of drugs, " Feinstein said last month upon the bill's passage.
Feinstein said her committee may ask Mr. Petraeus to testify before Congress.
WSJ: Congress to Investigate FBI's Handling of David Petraeus Inquiry
" And in the same interview, Senate Intelligence Committee Chairwoman Diane Feinstein said "the White House has to make a decision in this.
"These tickets are given for free to people, " Ms Feinstein said.
The swearing-in ceremony itself won't change from previous inaugurals, Feinstein said.
CNN: Officials: 2 million to show up to see Obama being sworn in
Senator Feinstein said over the weekend that she will come back from the holidays, next year, with a new Congress, and she will put forth such a proposal.
"There's a tentative agreement on a number of things, and we're waiting to see if it can get wrapped up, " Feinstein said in a brief interview at the Capitol.
The purpose of the hearing was "not to criticize, because I am a big fan of the FBI's, but to go back and see that we plug loopholes, " Feinstein said.
California's Dianne Feinstein said she spoke Wednesday with both Clinton and Obama, and while she decided to stay with Clinton for "as long as she's in this, " she was also realistic.
Feinstein has said she plans to introduce a bill in January that would place a ban on assault weapons.
CNN: Marine to senator: 'No ma'am,' I won't register my guns
For example, California Democrat Dianne Feinstein is said to introduce an amendment calling for a deadline for pulling U.S. troops out of Iraq.
Dianne Feinstein, said she intended to review proposals for "legislation to ensure that drone strikes are carried out in a manner consistent with our values" and she suggested something similar to the Foreign Intelligence Surveillance Court.
Dianne Feinstein of California said questions about the role of the Defense Department are significant in determining how to strengthen the nation's intelligence network.
If the CIA director "can't move the chairs on the deck of the Titanic, can't set strategy, can't bring the subtleties of a judgment to the decision makers, then you've got to change the structure, " said Feinstein, an Intelligence Committee member.
"It may well not be legal to carry any munitions on a drone, " said Senator Dianne Feinstein, D-California.
CNN: Drone use in U.S. may require new laws, Senate panel told
Dianne Feinstein, D-California, said she planned to raise the CIA detention and interrogation issue with Brennan.
Dianne Feinstein, D-California, said the tapes point to the "malevolent, malicious (and) venal" nature of al Qaeda.
Dianne Feinstein, D-California, said her father attended Taft Union High, which she has visited over the years.
Democratic consultant Kam Kuwata, who ran Ms. Feinstein's Senate campaigns, said she hadn't made a decision about entering the race.
Dianne Feinstein, D-California, has said she will introduce legislation to reinstate the assault weapons ban that expired in 2004.
CNN: Obama: Proposals to address gun violence due by January
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