Sponsored by Sens. Lindsey GrahamLindsey Olin GrahamSenators huddle on Russia sanctions as tensions escalate Juan Williams: It's Trump vs. McConnell for the GOP's future Biden's year two won't be about bipartisanship  MORE (R-S.C.), Mark BegichMark Peter Begich11 former Democratic senators call for 'meaningful reform to Senate rules' Harry Reid, political pugilist and longtime Senate majority leader, dies Alaska Senate race sees cash surge in final stretch MORE (D-Alaska), Jeff FlakeJeffrey (Jeff) Lane FlakeCruz to get Nord Stream 2 vote as part of deal on Biden nominees Democrats threaten to play hardball over Cruz's blockade Rubio vows to slow-walk Biden's China, Spain ambassador nominees MORE (R-Ariz.) and Mark PryorMark Lunsford Pryor11 former Democratic senators call for 'meaningful reform to Senate rules' Kyrsten Sinema is less of a political enigma than she is a strategic policymaker  Bottom line MORE (D-Ark.), the proposal is designed to clarify which cases of mental illness disqualify the patient from buying or owning guns.

The hope, Graham said, is "to ensure that those who have been declared an imminent danger to themselves or others aren’t legally able to obtain a firearm."

"I would expect overwhelming bipartisan support for our legislation,” Graham said.

Lending the bill a huge boost on Capitol Hill, the National Rifle Association (NRA), which helped write the bill, quickly released a statement Wednesday endorsing the measure.

"This bill will create accurate definitions of those who pose serious threats and should be barred from the ability to buy or possess a firearm, while protecting the rights of law abiding citizens and veterans," Chris Cox, executive director of NRA’s Institute for Legislative Action, said in a statement.

Under current law, licensed gun dealers are required to run potential buyers through the FBI's National Instant Criminal Background Check System (NICS) to screen those prohibited from buying or owning firearms. That list including felons, illegal immigrants, spousal abusers and the severely mentally ill.

The new Senate bill – the NICS Reporting Improvement Act of 2013 – is designed to clarify which people fall into the last group. It specifies that those involuntarily committed to a psychiatric hospital, those incompetent to stand trial in a criminal case, and those found not guilty by reason of insanity – among others – be banned from buying guns.

“Ensuring that more of these records are integrated into NICS will significantly improve the background check process,” Flake said.

The holes in NICS became glaring in 2007, when Seung-Hui Cho, a 23-year-old Virginia Tech student killed 32 students and teachers in one of the deadliest shooting rampages in the nation's history. A judge had declared Cho mentally ill two years earlier, but the state did not report its evaluation to NICS, allowing Cho to pass a background check by a licensed gun dealer.

Following that tragedy, Congress passed legislation providing states with financial incentives to report records of mental illness – along with other red-flag cases – to the FBI. Endorsed by the NRA, the NICS Improvement Amendments Act passed both chambers unanimously and President George W. Bush signed it into law in early 2008. But reporting by states remains voluntary.

Both Graham and Flake on Wednesday lamented that their home states are sitting on tens-of-thousands of mental health records that haven't been submitted to NICS. They applauded their state legislatures for taking steps to make such reporting mandatory – and encouraged other states to follow suit – but they are also not urging a federal requirement for state reporting.

A Senate aide familiar with the proposal said the sponsoring lawmakers did not want to require states to report cases to NICS because "as a general rule [states] don’t appreciate mandates from Washington."

Additionally, the senators did not want to place new burdens on states without paying the tab, which would have to be picked up by the states, the aide said.

Sponsoring legislation that has the backing of the NRA will likely help Graham, Pryor and Begich. Graham could face a primary challenge in his next reelection. Both Begich and Pryor are facing difficult reelection races in Republican-leaning states. 

—Mike Lillis contributed.