WASHINGTON -- Republicans began a new week pointing fingers at each other Sunday following a 16-day government shutdown and near-default that left the nation worse off and the GOP taking most of the blame.

But if there was a theme to the round of Sunday morning talk shows, it was the determination of most Republicans -- from Senate leaders to past and potential future presidential candidates -- to move on rather than focus on this month's failed battles.

"There will not be another government shutdown. You can count on that," Senate Minority Leader Mitch McConnell of Kentucky said on CBS' Face the Nation. "Shutting down the government, in my view, is not conservative policy."

"What we need to do is move forward with immigration reform, get a positive agenda for America," said Sen. John McCain of Arizona, the party's 2008 presidential candidate, on CNN's State of the Union. While fighting President Obama's health care expansion is important, he said, the emphasis should also shift to issues of taxes and spending.

That left Texas Sen. Ted Cruz, who instigated the government crisis by demanding an end to Obamacare and getting the Tea Party faction among House Republicans to go along, in a somewhat lonely position -- at least in the nation's capital.

Appearing on CNN and on ABC's This Week, the freshman senator blamed fellow Republicans for dooming the effort by speaking out against it rather than uniting behind it.

"I think it was unfortunate that you saw multiple members of the Senate Republicans going on television attacking House conservatives, attacking the effort to defund Obamacare, saying it cannot win, it's a fool's errand, we will lose, this must fail," Cruz said. "That is a recipe for losing the fight, and it's a shame."

Neither Cruz nor McConnell went after each other personally, but their sentiments were clear. McConnell, as he has done before, compared a second government shutdown following the one in 1995-96 to a second kick of a mule. Cruz defended it as a weapon in a tactical war.

There was little support for Cruz among other Republicans appearing on TV Sunday. Two fellow conservatives, Marco Rubio of Florida and Mel Blunt of Missouri, appearing on Fox News Sunday, said Health and Human Services Secretary Kathleen Sebelius should testify before Congress on Obamacare but should not -- at least not yet -- be forced to resign, as Cruz and some other Republicans have suggested.

And former Florida governor Jeb Bush, a potential 2016 presidential candidate, said the GOP needs to "show a little self-restraint" and let Obamacare play out, particularly since its government web site has left thousands of Americans unable to sign up for health coverage.

"Obamacare, flawed to its core, doesn't work," Bush said on ABC. "But we don't even hear about that because we've stepped on that message."