"The federal government should have stepped into this thing immediately to help make sure that the appropriate steps were being taken by BP [and] all federal agencies in support of the state government to try to get this thing cleaned up," Steele said. "And here we are almost a month and a half later and it's still spilling oil."
"Rand Paul is wrong," Kaine said. "It isn't un-American to hold somebody accountable for a massive environmental disaster."
Kaine also hit Paul for his comments about other federal regulations.
"Saying, as Rand Paul did ... that we needn't be so worried about things like mining regulations, I mean, this is a very important role the government has: to protect the safety of the environment and the health of citizens," Kaine said. "Rand Paul's statements along these lines are very, very troubling."
On the other hot-button political issue of the week, Kaine said Connecticut Attorney General Richard Blumenthal's statements indicating he served in Vietnam during the Vietnam War were "wrong."
"Those statements were wrong, period. They were wrong," Kaine said. "And it was very important for him to acknowledge that and clear that up."
Blumenthal is considered the frontrunner in the Connecticut Democratic Senate primary to be held on Aug. 10. He was endorsed by the state's Democratic convention on Friday.
Steele decried the "credibility gap" that Blumenthal had opened up.
"At a time when the American people are clearly rebelling against the same-old, same-old in politicians," Steele said, "Blumenthal is not the kind of guy I think they want to send anywhere, let alone to Washington to serve at this time, so I think there is a big credibility gap here."
Blumenthal's misstatements were first reported by The New York Times online on Monday.
Steele said that despite a recent loss in Pennsylvania's 12th district, Republicans would win the House seat there in November, but he wasn't so sure about taking control of Congress.
On Tuesday, Democrat Mark Critz won the special election to replace the late Rep. John Murtha, D-Pa., but Steele said it was a conservative district that the GOP would win in five months.
"In November, we'll get that seat back because, guess what, independent conservatives get to play then and that will be a very different race," Steele said.
"Are you going to take the House back in November?" Tapper asked the RNC chairman.
"We're working very hard to do that, but, as you can see, you know, with some incumbents going down in primaries, and newer players coming to the table, that model is still being built out for us. But, absolutely, we're in the hunt," Steele said. "Just as he's in the hunt to protect, we're in the hunt to take."
"Jake," DNC chairman Tim Kaine said, "we're going to hold on to both Houses."
Kaine equivocated on whether the White House has a responsibility to discuss what it offered Rep. Joe Sestak to not run -- and ultimately win -- against Sen. Arlen Specter in the Pennsylvania Democratic Senate primary for Spector's Senate seat. Sestak has indicated he received an offer of some sort.
"Does the White House have a responsibility to own up and talk about what exactly was offered?" Tapper asked the DNC chairman.
"I don't know that they do," Kaine said, adding that the White House now needed to work to make sure Sestak is Pennsylvania's next Senator.