In their appearances on Fox News Sunday, Kyl said he thinks financial regulatory reform could be achieved with support from both parties if each side is willing to give up votes from members of their parties' fringes.
Kyl said there were signs of burgeoning bipartisanship on the issue until Senate Banking Committee Chairman Christopher Dodd, D-Conn., "decided to pull back and present just a partisan bill."
"Now, the understanding was that he was losing some votes on his far left by working with Republicans," Kyl said. "But it seems to me that on something like that, where there is an opportunity to work together -- we all agree we need to do some things -- it would be far better to try to do it with a broad middle coalition that does include Republicans.
"And if that means you lose a few votes on the far left and maybe you don't get all of the votes on the right, so be it. At least you've done something the American people would like to see us do. But as of right now, that too seems to be drifting in a very partisan direction. And if it does, it will be hard to pass."
But Specter responded he thinks Kyl espoused an overly positive view of the situation.
"Only one Republican, Senator (Bob) Corker, (R-Tenn.) would step forward and negotiate with Chris Dodd. I think Senator Kyl paints a rosier picture about the prospects for bipartisan support than exists," Specter said. "A real effort was made."
Saying both parties "for a long time" have been controlled "by people on the fringes," Specter said falling public approval ratings may be "a real impelling factor to produce some bipartisanship cooperation."
Kyl said he also thinks Republicans will support the extension of unemployment benefits but will "look very carefully" at other spending plans. He said he'd like to see the Democrats extend their proposal for a zero capital gains tax rate for small businesses to all businesses. He added if President Barack Obama asked Congress to freeze all taxes "I think you'd see the stock market skyrocket the next day because business would know that taxes will be stable and that they have the ability to raise capital and invest it in their businesses."
Notable deaths of 2014 [PHOTOS]