Story highlights Texas senator believes cuts may not be as bad for defense as the Pentagon says

John Cornyn could face criticism from fellow Republicans with GOP strong on defense

Pentagon would absorb half of the automatic, government-wide spending cuts

Cuts due to take effect on Friday absent congressional action to avert them

Anticipating possible political backlash if forced federal spending cuts kick in as expected later this week, the Senate's No. 2 Republican said Monday that he is preparing a message he plans to hit hard: The cuts are not going to have as negative an impact as the Pentagon and others in the Obama administration are saying.

Sen. John Cornyn of Texas said he plans to make the case to other Republicans and the public that despite warnings from the Pentagon that the mandated cuts will be devastating, the overall amount of defense spending will actually still rise.

Cornyn conceded that until now he had been parroting what Defense Secretary Leon Panetta continuously warns -- that automatic, government-wide cuts could jeopardize national security.

But the veteran senator said he looked into it and will now argue that even if the cuts go through on March 1, the Pentagon will still see its budget go up

Cornyn's preview of what he hopes will be a Senate GOP argument is significant since defense cuts are usually something Republicans adamantly oppose. He will surely run up against some in his party who strongly disagree.

To be sure, Cornyn called himself a defense "hawk" and did say the role of the federal government should be first and foremost to protect American citizens.

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But he also believes that the deficit should be paramount since the United States has ended its fighting in Iraq and is winding down the war in Afghanistan.

He added that if "God forbid" another 9/11 happens, Congress would act.

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Still, Senate Republicans are considering a proposal this week that could alleviate some impacts of the cuts by giving the president flexibility to decide where they would occur.

However, GOP sources tell CNN that Republicans have not yet worked out among themselves whether their measure would give the president that flexibility on all domestic agencies and programs or just on defense.

GOP sources say they are likely to work that out when Senate Republicans huddle for their regular lunch on Tuesday.

The $85 billion in forced spending cuts were written into law intentionally to be indiscriminate.

The law does not allow, for example, the Pentagon to keep funding going for a ship building program by shifting money being spent on a military golf course. And it does not allow the Health and Human Services Department to keep children in Head Start programs by cutting deeper in another agency.

Part of the reason Senate GOP leaders have not decided yet how broad that flexibility should be -- whether it should apply just to the defense cuts, as many Republicans want, or to domestic cuts as well — is due to differences in opinion among Republicans over how much power to give the president.

But it is a key decision, since granting the president flexibility in cuts across the board could make it hard for conservative Democrats, such as those from defense industry-rich Virginia, to oppose.

That's because such an approach could soften the political burden for those Democrats who would be able to argue to their constituents they did everything possible -- including providing flexibility to the White House -- if economic damage ripples through their states.

But one influential Republican senator told CNN on Sunday that he opposes giving the president so much flexibility because it undermines the decision-making authority of Congress

"I say to my Republican friends, if you want to give the president flexibility as to how to exact these cuts in defense spending, then why don't we go home and just give him the money? I am totally opposed to that," Sen. John McCain , R-Arizona, said on CNN's "State of the Union." "We spent too long on defense authorization and finding out what this country needs to secure this country without saying, 'Hey, well we'll just let the president have the, quote, flexibility.'"

A competing Senate Democratic proposal would replace the automatic spending cuts with a mix of tax increases on wealthier Americans and more targeted spending reductions than those currently required. Democratic leaders believe it will get more than 50 votes -- so they will be able to claim it won a majority in the chamber -- but will fall short of the 60 it would need to win Senate approval.

In the meantime, both sides are preparing for no change -- and for forced spending cuts to take effect Friday.

Democratic leadership sources admit that whether or not they can ultimately do anything to change the way across-the-board cuts are enacted will depend on the level of public outcry -- and media coverage.

Democrats admit the impact may not be felt for at least a month, maybe more.

Assuming no legislation is passed to alter the cuts this week, sources in both parties say they are already looking ahead to the next big deadline on March 27, when the funding for the government runs out.

A Democratic congressional source tells CNN that at this point, Democrats do not believe the White House wants to use that debate to revisit forced spending cuts, but the source said that could change depending on public reaction to the cuts.