Obama cited the major provisions of his package of gun proposals, including background checks on all firearms sales, a ban on semi-automatic weapons that mimic military weapons, and limiting ammunition magazines to 10 rounds.
In the most emotional moment of the speech, he listed people whose lives have been "torn apart by gun violence." They included Pendleton's parents, Giffords, and the families of the Newtown victims.
Obama repeatedly insisted "they deserve a vote" as the audience cheered loudly.
But the powerful National Rifle Association and legislators from both parties oppose key provisions of Obama's plan.
Rubio echoed the NRA position that "unconstitutionally undermining the Second Amendment rights of law-abiding Americans is not the way to" reduce gun violence.
Meanwhile, NRA President David Keene conceded there would be votes on some issues, but he accused Obama of playing up the emotional side of the issue to try to force through gun control laws before they can be properly debated.
On foreign policy, Obama announced that this time next year, another 34,000 U.S. troops will have returned home from Afghanistan. The move will reduce by more than half the current force level there of 66,000 troops as Afghan forces prepare to take the lead in combat missions. The plan is for all U.S. combat troops to leave by the end of 2014.
On climate change, Obama promised executive action if Congress failed to address what he called a litany of evidence that the nation and the world face such as more frequent and powerful storms, wildfires and drought.
On cybersecurity, Obama signed an order on Tuesday making it easier for private companies controlling critical infrastructure to share information about cyber attacks with the government. In return, the government will share certain information with companies about attacks believed to be occurring or that are about to take place.
Congress has failed to pass any of the dozens of bills aimed at meaningfully securing critical infrastructure from cyber attack.
Rubio is promoted as the new face of the Republican Party due to his Hispanic heritage and strong communications skills.
Obama won overwhelming support from the Latino vote in defeating GOP challenger Mitt Romney in the November election.
Rubio is leading an effort by some Republicans to shift party policy on immigration reform by accepting the concept backed by Obama and Democrats that the nation's estimated 11 million undocumented immigrants should have a path to legal status.
However, he neglected to mention specifics of an immigration reform plan in his response Tuesday night.