In statements and attack ads, the groups have sought to undermine Hagel's nomination in the weeks leading up to his confirmation hearing on Thursday before the Senate Armed Services Committee. His opponents face a tough challenge as Democrats have begun to rally around the president's choice, and the party has the majority votes to confirm the former two-term Nebraska senator, barring surprises.
Here's a look at the validity of some of the criticism of Hagel.
THE CLAIM: "We live in a dangerous world. Iran, North Korea, even Russia. But Barack Obama's nominee for secretary of defense wants America to back down. An end to our nuclear program. Devastating defense cuts. A weaker country." An ad being run by Americans for a Stronger Defense in the home states of five Democratic senators up for re-election next year Alaska's Mark Begich, Arkansas' Mark Pryor, Louisiana's Mary Landrieu, Colorado's Mark Udall and North Carolina's Kay Hagan.
THE FACTS: Hagel has not proposed ending the nuclear weapons program, though he has supported deep cuts.
Hagel was co-author of a May 2012 study by the advocacy group Global Zero that called for an 80 percent reduction of U.S. nuclear weapons and elimination of all nuclear-armed intercontinental ballistic missiles.
The group argued that with the Cold War over, the United States needs no more than 900 total nuclear weapons. Currently, the U.S. and Russia have about 5,000 each, either deployed or in reserve. Both countries are on track to reduce the deployed strategic warheads to 1,550 by 2018, the number set in the New START treaty that the Senate ratified in December 2010.
The study said: "These steps could be taken with Russia in unison through reciprocal presidential directives, negotiated in another round of bilateral arms reduction talks or implemented unilaterally." The report was by Hagel, former ambassadors Richard Burt and Thomas Pickering, retired Gen. James Cartwright, a former vice chairman of the Joint Chiefs of Staff, and retired Gen. John J. Sheehan.
An arsenal of 900 nuclear weapons would not be an "end" to the U.S. nuclear program, but Hagel and the organization did raise the possibility of unilateral reductions. In a statement Monday, Burt and others defended Hagel and dismissed suggestions that they were "unilateralists."
The group running this anti-Hagel ad was formed recently and offers little information about itself on its website. Board member Mauricio Claver-Carone also is director of the US Cuba Democracy Advocates in Washington and favors tighter restrictions on the Castro government.
THE CLAIM: "Opposition is growing even more due to his support for sequestration of the military: huge budget cuts that the Joints Chiefs have already warned the Senate Armed Forces Committee would result in a 'hollow force.'" A Jan. 22 statement from Move America Forward, a California-based group founded by conservatives in 2004 to show support for U.S. troops.
THE FACTS: The group offered no evidence Hagel supports sequestration, the budget mechanism that will mean automatic, across-the-board spending cuts March 1 if Congress does not act to avert them. The White House says he opposes the mechanism, which came into play after Hagel left the Senate.
To be sure, Hagel has spoken about cutting Pentagon spending. In a 2011 interview with the Financial Times, Hagel said, "the Defense Department, I think in many ways, has been bloated" and "has gotten everything it's wanted the last 10 years and more."
The base defense budget has nearly doubled over 10 years, to about $528 billion this year. That doesn't include the billions spent on the wars in Iraq and Afghanistan.
Obama and congressional Republicans agreed in August 2011 on a deficit-cutting plan that would cut $487 billion from projected defense spending over 10 years. Democrats and Republicans also voted for automatic cuts of $55 billion this year if a special congressional panel can't come up with a sweeping deficit-cutting plan.
Defense Secretary Leon Panetta has warned against the approach of across-the-board cuts, and Hagel has given no sign that he has a different view.
THE CLAIM: "Now Hagel sits on the board of Chevron, which receives hundreds of millions in Pentagon contracts. ... How can Chuck Hagel run the Pentagon with so many ethical questions about his own record?" Ad by the American Future Fund, which is running a "Hagel No" campaign. The group describes itself as advocating conservative, free-market ideals.
THE FACTS: It's widely assumed that Hagel will be leaving the Chevron board, a move common for nominees who face the prospect of such ethical conflicts. The Senate Armed Services Committee has some of the most stringent rules for nominees for senior civilian positions in the Defense Department. The panel requires nominees to divest all financial interests in companies doing business with the department. Stepping down from any board would certainly be required.
The committee bases its decisions on the Defense Department list of companies with contracts valued at $25,000 or more. The list is 330 pages long and includes Chevron.