His latest move may appeal to more mainstream GOP voters: According to a CNN/Opinion Research poll from last year, about 70 percent of Republicans consider themselves hawks rather than doves.
But it's less clear is how his base voters will react. According to a 2013 poll from Reason magazine, self-identified libertarians were much more supportive of defense spending cuts than the public overall or Republicans. The poll found that 60 percent of libertarians supported cutting defense as a way to balance the budget, compared to 49 percent of the overall public and 29 percent of the country as a whole.
How far is the new Paul policy from his old positions? In 2011, back in the pre-sequester era, he called for about a 23 percent reduction in defense spending, including cuts to overseas operational costs and war spending from $159 billion to about...zero.
The amendment Paul put forward Thursday would allocate $697 billion for defense in the next fiscal year. Paul adviser Doug Stafford said the amendment is "response to others in both chambers who are attempting to add to defense spending - some way more than Senator Paul's amendment - without paying for it."
Paul said last month at the Conservative Political Action Conference that national defense is a top priority, a position he has stressed on the campaign trail -- where voters have peppered him with questions about the Islamic State and Iran.
"Senator Paul believes national defense should be our priority. He also believes our debt is out of control. This amendment is to make sure people understand that if you believe we need more funding for national defense, you should show how you would pay for it. No one should be seeking increased funding for anything by increasing our debt," Stafford said in a statement.
Paul himself has been trying to split the difference between his former position and his new approach, to make the case that he's still a defense budget hawk -- even if he's not calling for the cuts he has in the past. Last week, at an event in Exeter, N.H., he told voters that military spending is not a "blank check."
"When we look at the overall military budget you’ll find people in our party who say it needs to be $600 billion or $650 billion. We need to look at it in context. We have doubled the amount of military spending since 2001. Doubled it," Paul said. "We spend more on our military than the next 14 countries combined. This includes Russia, China, all these potential rivals of ours. We spend more than the next 14 combined. So I think we do need to put it in context but I don’t want us to be weak either. I want us to defend ourselves."
And he told voters in Manchester the military budget is still inflated.
“I think national defense is a vital part of the federal government, but national defense is bloated as well," Paul said. "It’s got a vast increase in bureaucracy just in the last 30 years at the Pentagon, so when I say I want to look at all parts of the government I truly do. I’m for auditing the Fed, but I’m also for auditing the Pentagon. I think it’s insulting that the Pentagon says frankly, we’re too big to be audited. If you’re too big to be audited there’s a problem.”
Paul proposes that the increased money would be offset by cutting $21 billion from foreign aid -- a position he has taken before, calling for "not one penny more" to "haters of America" including China and Pakistan. Paul sees foreign aid as being closely tied to defense, as it can be used to bolster portions of foreign military programs. In 2011, he called for an end to all foreign aid, but moderated last year, proposing to freeze it at $5 billion.
He also wants to ax $14 billion from the National Science Foundation and climate change research, $10 billion from the EPA and Department of Commerce, $20 billion from the Department of Education and $41 billion from HUD.
The Kentucky Republican has called for abolishing many of these departments.
"I’d get rid of departments. I’d cut down government. I’d close the Department of Commerce," he said in Manchester. "You wouldn’t even notice it was gone. That’s $30 or $40 billion. I’d shut down the Department of Education. I don’t think you’d know it’s gone."
But the fact that those cuts are unlikely to happen is less relevant to Paul's presidential fortunes than the fact that his move now puts him on more even footing with other potential 2016 rivals -- notably, Sen. Marco Rubio (R-Fla.), who has also called for increasing military spending.
The challenge in maintaining his new policy balancing act -- appealing to a more hawkish majority, while holding on to a libertarian base that's less keen on military spending boosts-- was apparent in New Hampshire last weekend.
Danny Gorman, 68, of Rochester, met with Paul at the Pink Cadillac Diner in his hometown. Gorman, a Vietnam veteran, said he agreed with Paul's more anti-interventionist stances.
"Keep our boys at home," he said. "We've got enough troubles at home."
Others, tuning in at other stops for Paul's stump speech, sounded approving notes on his evolution.
“Foreign policy is a tough nut to crack, but I truly support what he said. We just can’t ignore our allies and suck up to our enemies,” said Bob Graham of Milton, N.H.