Even if the bill in question does make it through the Senate (which doesn't seem particularly likely given the current makeup of that chamber), it is extremely unlikely that President Obama would sign it as he's made previous statements against CC and comes from the only state in the country which still has no legal provision for a private individual to carry a loaded firearm.
If this bill goes any further, I see it happening after the next election and then only if the political makeup of the Senate and White House is very different from what it is today. Even then, we could expect rather tenacious opposition because the chances of the "usual suspects" such as Feinstein, Boxer, Schumer, Pelosi, Rush, and McCarthy all losing re-election are very, very remote.
I think that the much more likely path for broadening carry rights is the judiciary and agreements between the states, and I'm not all that convinced that's not the way it should be.
Smith, and Wesson, and Me. -H. Callahan
Well waddaya know, one buwwet weft! -E. Fudd
All bad precedents begin as justifiable measures. -J. Caesar