Childers, D-Booneville, was first up to bat, signing a pledge to protect Social Security from the Wall Street barons "who got us into this financial mess."
A few minutes later, Republican Nunnelee of Tupelo echoed the pledge and also challenged Childers to reconsider repealing the nation's new health care law.
For months, Childers has urged Nunnelee to tell the voters if he will fight Social Security privatization, which some Republicans suggest is one way to give people more control over their futures by allowing them to invest their contributions.
"I'm happy to see that after 22 months of his waffling," Nunnelee planned to sign the protection pledge, Childers said when asked about the impending rival news event.
Childers suggested Nunnelee's apparent change of heart came after Childers released a poll Tuesday showing he was ahead of Nunnelee by 5 percentage points.
At his news conference, Nunnelee said he decided "months ago" to oppose privatization.
They also oppose raising the retirement age and cutting benefits or raising taxes.
Nunnelee said he wants to repeal the new health care law and start over again.
Childers has said he'd prefer to make changes later, if they are needed, rather than scrapping the landmark legislation, which he voted against.
Childers and Nunnelee meet on the Nov. 2 general election ballot with seven other independent candidates or non-mainstream party nominees.
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