Correction Appended

Updated: 3:15 p.m.

Democratic and Republican Senators on Sunday voiced concern over the direction of health care reform legislation, even as they emphasized support for an overhaul of some kind.

On CNN’s “State of the Union,— Sens. Dianne Feinstein (D-Calif.) and Dick Lugar (R-Ind.) both said while they want Congress to act, they worry about the unintended consequences of sweeping reform.

“It’s complicated,— Feinstein said. “If you change the Medicaid rate, for example, it has an impact on California between $1 billion and $5 billion a year. Now, how could I support that? Because it would take down the state.—

And Feinstein also said she doesn’t believe President Barack Obama has enough support in the Senate to clear a bill, saying: “To be candid with you, I don’t know that he has the votes right now. I think there’s a lot of concern in the Democratic caucus.—

Meanwhile, Lugar urged Obama to halt his push to pass health care reform this year, saying fixing the nation’s faltering economy should take precedence.

“I don’t have the slightest idea what is in either of the two bills in the committees. None of us do because much of it hasn’t been written, still being drafted,— Lugar said. “People are scoring something that doesn’t exist. What I would suggest is we hang on now for a period of study so that we find literally what the alternatives are.—

Speaking on another program, Sen. Chris Dodd (D-Conn.), who is managing the markup of a reform bill in the Health, Education, Labor and Pensions Committee, reiterated his support for the government-run insurance option. Still Dodd, appearing on ABC’s “This Week,— suggested that his panel would continue to steer a liberal course on health care and conceded that passing a bill will be difficult.

“This is a difficult road, I’ll be the first to admit it,— said Dodd, who is filling on the committee for Sen. Edward Kennedy (D-Mass.), who is battling brain cancer.

Obama has asked that Congress pass a health care reform bill no later than Oct. 15. House and Senate Democratic leaders are aiming to clear bills out of their respective chambers by the end of July, although meeting that timeline will be challenging. The process for approving reform in the Senate calls for HELP and Finance to pass separate bills and then merge them into a single vehicle for floor consideration.

Sen. Chuck Grassley (R-Iowa), ranking member on the Finance Committee, said on “State of the Union— that he is confident that a bipartisan bill will emerge. Grassley is working with Finance Chairman Max Baucus (D-Mont.) to craft a compromise bill. The committee was prepared to mark up its health care package this week but postponed action until after the July Fourth recess.

“We feel that we will be able to put together a bipartisan plan that will do what everybody wants to do — accessibility and affordability — and we’ll be able to pay for that,— Grassley said.

“We’re in the position of dialing down some of our expectations to get the costs down, so that it’s affordable, and most importantly, so that it’s paid for,” Grassley added.

And perhaps in some of the harshest rhetoric of the day, Sen. Lindsey Graham (R-S.C.) said that any Senate legislation containing a public plan option was a non-starter. Congressional Budget Office estimates showing it would cost more than $1 trillion to implement “were a death blow to a government run health care plan,” he argued.

“We do need to deal with inflation in health care, private and public inflation, but we’re not going to go down to the government owning health care road in America and I think that’s the story of this week,” Graham said. “There’s been a bipartisan rejection of that.”

Correction: June 21, 2009

An earlier version of this story mistakenly referred to comments from Sens. Ben Nelson (D-Neb.) and Kent Conrad (D-N.D.) on health care. Nelson and Conrad offered those remarks on June 14, not this Sunday.