Senators of both parties said Tuesday that despite the nation’s bleak fiscal situation, they want President Barack Obama’s next budget chief to be pretty much like the guy who has held the job for the past year and a half.

To be sure, Senate Republicans will grill Obama’s nominee to replace Office of Management and Budget Director Peter Orszag, using the confirmation process to cast a critical eye on the administration’s policies. However, Orszag managed to maintain his reputation as a fiscal hawk during his time in the administration, with some Republicans saying there was little Orszag could do to control red ink while working for a free-spending boss.

“The OMB director’s ultimate responsibility is to do what the president tells him to do,” said Sen. Judd Gregg (R-N.H.), ranking member of the Budget Committee.

Orszag’s departure as director of the OMB is not official, but Members generally assume he will be gone within the next few weeks.

Both Democrats and Republicans praised Orszag’s work guiding the OMB during a time of great financial strain for the country, noting the difficulty of the job even in times of economic prosperity. But Senate Republicans expressed frustration that Orszag and his reputation for fiscal discipline while heading the Congressional Budget Office failed — in their view — to hold greater sway with the president.

Senate Republicans said they would use the confirmation hearings for Orszag’s replacement as a proxy to question the effect of the new health care law on the budget deficit and how the administration plans to address the growing federal debt.

“We’re going to make them defend this health care bill, which I think makes everything worse on the fiscal side,” said Sen. Lindsey Graham (R-S.C.), a member of the Budget Committee.

Democrats also suggested the need for Obama to get the $1.6 trillion deficit and projected $13 trillion debt under control. They are likely to join the GOP in asking tough questions of whomever Obama nominates to succeed Orszag.

Centrist Sen. Tom Carper (D-Del.) praised the Obama administration’s efforts to rein in Washington’s checkbook. But he also offered the White House — as well as Congress — some subtle criticism, suggesting that both could do more to embrace Orszag’s very public and long-held views on the need for fiscal austerity.

Additionally, Carper said he would prefer Orszag to remain as OMB director through year’s end for the sake of continuity during the appropriations process and the debate over the fiscal 2011 budget resolution.

Carper pointed to an instance when Orszag testified before the Senate Finance Committee with a pitcher of diet soda by his side, rather than the customary water. Carper likened that story to what President Abraham Lincoln told critics who questioned his hiring of Ulysses S. Grant, an alcoholic, to be his top Civil War general. Lincoln told his critics to find out what Grant was drinking and give it to the rest of his generals.

“The president needs to find out what Orszag is drinking and give it to the rest of the Cabinet — and some for us,” Carper said.

Budget Chairman Kent Conrad (D-N.D.) called Orszag’s decision to leave the OMB “a loss for the country.” He said Orszag has a command of the issues and an understanding of the necessity to reduce deficits and debt, as well as a comprehension that economic recovery comes first.

Conrad, a budget hawk who on occasion hasn’t been shy about putting this administration on the spot over its fiscal policies, said he would like to see someone similar to Orszag succeed him as OMB director. The Budget chairman declined to drop names, but he did say he would prefer CBO Director Doug Elmendorf stay where he is.

“We need him badly there,” Conrad said, adding that he expects the confirmation process to be difficult. “That’s always a challenge around here — confirmations.”

Sen. Tom Coburn (R-Okla.), who has built his career around the idea that Washington spends too much money, said he would prefer Obama nominate someone who “knows how to cut spending” and said hopes his GOP colleagues subject Obama’s nominee to tough questioning.

Sen. Blanche Lincoln (D-Ark.), who faces a tough re-election battle this fall, said she would like someone similar to Orszag in intelligence and someone who has a deep background in budget and fiscal issues.

Gregg views Orszag as one of the few administration officials with credibility on the deficit and the debt. “When he left CBO, he certainly had quite a reputation as a fiscally responsible voice around this place,” Gregg said.

However, Gregg said Orszag’s philosophy on government spending as he interprets it is inconsistent with supporting the Obama administration’s domestic priorities, particularly the $787 billion stimulus package and the new health care law, projected by CBO to cost about a trillion dollars over the next decade.

Gregg added that much of what the administration did “is the opposite of what somebody who is fiscally responsible would support.”