Biden's criticism alluded to a book Ryan, the chairman of the House Budget Committee, co-wrote with House Majority Leader Eric Cantor (R-Va.) and Majority Whip Kevin McCarthy (R-Calif.) titled Young Guns: A Generation of Conservative Leaders.
The GOP's Young Guns program singles out for support Republican candidates running for office to bolster GOP ranks in Congress.
Biden has repeatedly charged policies supported by Romney, Ryan and the Republicans in the House of Representatives would seriously harm the middle class. The vice president reiterated much of that criticism in his Thursday speech, saying that the Supreme Court's ruling on abortion in Roe v. Wade wouldn't survive four years of a Romney administration.
Brendan Buck, a spokesman for Ryan, called Biden's remarks "over-the-top."
"Today’s over-the-top rhetoric by Vice President Biden is disappointing, but not all that surprising," Buck said in a statement. "In the absence of a vision or plan to move the country forward, the Vice President is left only with ugly political attacks beneath the dignity of the office he occupies. Mitt Romney and Paul Ryan will bring serious leadership to Washington that will focus on an agenda of job creation and economic growth that benefits all Americans."
Biden spokeswoman Amy Dudley stressed that the vice president's remarks about bullets were not meant to be taken literally.
"The Vice President’s exchange with an audience member today was clearly a reference to how the policies discussed in Paul Ryan’s book, Young Guns would devastate the middle class," Dudley said in a statement. "Given that people don't assume that Paul Ryan is literally a gun, it probably makes sense not to assume that Joe Biden was speaking literally about bullets."
—This story was updated at 5:34 p.m.