Sen. Carl Levin (D-Mich.), chairman of the Senate Armed Services Committee, pressed the Romney camp on whether the candidate would take the Taxpayer Protection Pledge from Grover Norquist. The pledge opposes any and all tax increases for individuals and businesses, as well as any reductions in tax credits without matching reductions in tax rates.
Romney refused to sign the Norquist pledge during his 2002 gubernatorial campaign in Massachusetts, but did run on a platform to cut the state's deficit without increasing taxes.
Levin said no modern-day president, including Ronald Reagan, could abide the mandates outlined in the Norquist pledge while simultaneously pushing through a deficit-reduction plan.
"That is an extreme position," he said during his speech at the National Press Club.
He said an anti-tax stance becomes even more difficult to hold when trying to stop the automatic budget cuts set to hit the Pentagon over the next decade.
Romney has slammed the $500 billion in automatic cuts that are scheduled to take effect through sequestration, calling them “reckless.” The move has put the United States “on a path to a hollow military," according to the Romney campaign.
Romney has said increased military spending, particularly in the Navy's fleet, would be a top priority should he win the White House in November.
Levin said the deficit-reduction Romney is seeking simply wouldn’t be possible if Republicans continue to balk at including revenue increases as part of some alternative to sequestration.
"The big issue is revenue," Levin said. Romney and the Republican Party must "gradually recognize there can be no real deficit reduction . . . without revenue [increases]."
Sens. John McCain (R-Ariz.) and Lindsey Graham (R-S.C.) have been pressing the need for tax increases in any sequestration alternative to their GOP colleagues.
A number of senators have been spending the past few weeks preparing a slew of sequestration options in anticipation of the coming political fight over the issue during the lame-duck session of Congress after the election.
After his speech, Levin said he has discussed those plans with both McCain and Graham in recent weeks.
The Michigan Democrat declined to comment on the nature of those talks, but said "there is evidence" that a bipartisan deal on sequestration could be reached that would include concessions on tax increases.
Senate Democrats and Republicans are on the same page on "90 percent of the things" that need to be included in any potential alternate sequestration deal, including tax increases, according to Levin. "There's a lot of things that can be agreed to," he told The Hill.
Sen Joe Lieberman (I-Ct.) told The Hill on Tuesday the sequestration debate in the Senate has reached a point where tax increases can no longer be ignored.
Any plan to stave off defense cuts under sequester "is not going to pass unless you have a mix" of spending reductions and revenue increases.
For his part, Lieberman said he would support the mix proposed in the deficit reduction plan pitched by former Sen. Alan Simpson (R-Wyo.) and former White House Chief of Staff Erskine Bowles.
Roughly two-thirds of the Simpson-Bowles plan was focused on federal spending cuts to reduce the national deficit, with the remaining one-third focused on tax increases.
That plan could serve as a legitimate blueprint for any alternative sequestration plan the Senate may come up with, according to Lieberman.
When asked if Senate Republicans would support any sequestration plan that included tax increases to offset defense cuts Lieberman replied: "I hope so . . . or else its not going to pass."
— This story was updated at 4:53 p.m.