The new initiative, to be called the National Council for a New America, will involve an outreach by GOP officials including John McCain, the 2008 Republican presidential nominee, and Mississippi Gov. Haley Barbour, former national GOP chairman, CNN reported.
Others on the "panel of experts" will include former Florida Gov. Jeb Bush, younger brother of former President George W. Bush; Louisiana Gov. Bobby Jindal and former Massachusetts Gov. Mitt Romney.
"However, this is not a Republican-only forum," reads a letter announcing the new effort. "While we will be guided by our principles of freedom and security, we will seek to include more than just our ideas."
Meanwhile, a debate broke out among Republicans Wednesday on what to do to make up for the loss of Pennsylvania's Specter to the Democrats.
The question seemed largely centered on whether the party should purge moderate voices like Specter and embrace its conservative roots or seek to broaden its appeal to regain a competitive position against Democrats, The New York Times said.
Some conservatives applauded Specter's departure, saying it cleared the way for the party to distance itself from a record of expanding government during the Bush years and to re-emphasize the call for tax cuts and reduced spending.
But some Republican leaders argued that the GOP would be permanently marginalized unless it showed flexibility on social and economic issues.