Washington (CNN) – Most Republicans demanding to slash federal spending won't entertain the idea of taking a possible standoff with President Obama so far that the government shuts down.
But the top Republican on the Senate Budget Committee told CNN Monday he's not ruling out that possibility "if the President just stonewalls – refuses to pass anything that will be responsible."
In 1995, when Republicans controlled all of Congress and a spending stalemate resulted in a government shutdown, President Clinton went on to win re-election.
Most Republicans remember that as a politically disastrous move they don't want to repeat. Sessions says there was an upside – the country's fiscal condition did get better.
"It worked out good for the country. We had three years of balanced budgets that would never have happened had they not fought that hard in Congress so I think that Congress does have to fight," said Sessions.
Sessions said he is worried that the "gulf" between what Republicans want in spending cuts and what President Obama will tolerate may be too hard to bridge.
"It does appear that the president is a man of the left. He believes in government - he's still talking about it now – investments, which are spending programs," said Sessions.
One of the first fights over spending will come over whether to raise the debt ceiling to avoid the U.S. from defaulting on its debt – now totaling more than $14 trillion.
Many Republicans have said they will vote to do that only if the president agrees to cut spending.
The Alabama Republican says he wants no less than a 10 percent across the board spending cut in exchange for his vote to raise the debt limit.
"I truly believe that the debt limit is one of those points in which it will require the administration to meet with Congress and ask and answer the question of how we can continue at this rate, what changes can we make," said Sessions.
House Republican leaders have pledged to cut spending back to 2008 levels by the end of this year, which they now say adds up to $50 or $60 billion.
Sessions also told CNN he likes an idea proposed by House conservatives in the so-called Republican Study Group to go well beyond that - cut spending back to 2006 levels, which they say adds up to $2.5 trillion in savings over 10 years.
"Yes to go back to 2006 levels, that's just four years ago," said Sessions. "The country isn't going to sink into the ocean if we reduce spending that much. That would make a significant difference in our deficits, sending a message to the world that we're serious and I think create more confidence in our economic growth."