Updated 9:14 p.m. | Sen. Rand Paul doesn't have a problem with increasing the defense budget, but he wants real offsets.
And the Kentucky Republican, who seems to be gearing up for an April 7 announcement about a run for the White House, proposed an amendment to the budget resolution just before the Senate adjourned Wednesday to do so.
"This amendment is in 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. Senator Paul believes national defense should be our priority. He also believes our debt is out of control," Paul senior adviser Doug Stafford said in a statement.
"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," Stafford said. "No one should be seeking increased funding for anything by increasing our debt."
Paul's amendment garnered a mere four votes in the Senate.
There have been several other efforts to increase the level of defense spending ahead of the Senate's budget vote marathon known as the vote-a-rama, including from other prospective presidential contenders.
Republicans Marco Rubio of Florida and Tom Cotton of Arkanas have teamed up on an effort to increase the Pentagon budget that they outlined in a CNN opinion piece Thursday morning. Their amendment would raise the defense levels to the fiscal 2012 request level, Rubio and Cotton said.
"Now that Republicans control both house of Congress, it is time to support a defense budget that actually reflects the world in which we live, not the world the way we wish it was. Until now, our approach as a country and a party since the Budget Control Act has not been one of American strength. Continuing on the current path will only invite war and conflict through weakness," the senators wrote. "We need to heed the bipartisan warnings of our nation's military leaders and get back on track toward a defense budget that reflects the realities of the challenges we face and is worthy of our brave men and women in uniform."
Rubio's effort garnered 32 votes.
Sen. Lindsey Graham, R-S.C., spearheaded the effort in the Budget Committee along with Sen. Kelly Ayotte, R-N.H., to increase the Overseas Contingency Operation account budget level to $96 billion. Their frequent colleague John McCain, R-Ariz., told CQ Roll Call late Wednesday that he continued to work to build support for an amendment that would nullify a point of order against the increased war money.
Related: Voting Marathon: More Test Marketing Than Attack Ads Vote-a-Rama Presents Political Peril for Vulnerable Incumbents The 114th: CQ Roll Call's Guide to the New Congress Get breaking news alerts and more from Roll Call in your inbox or on your iPhone.