Isakson: Gun bill deserves an up-or-down vote

"Some back in Washington are already floating the idea that they might use political stunts to prevent votes on any of these reforms,” Obama said. “They’re not just saying they’ll vote ‘no’ on ideas that almost all Americans support. They’re saying they won’t allow any votes on them at all. They’re saying your opinion doesn’t matter. And that’s not right.”

The president traveled back to Washington with a dozen family members of victims of the Sandy Hook elementary school shooting, who will spend the week lobbying senators on Capitol Hill. Isakson said Tuesday he would meet with some of the victims' families later in the day.

"The heart and soul of every American goes out to the families of those who lost their lives in Sandy Hook, and they deserve a right to sit down and talk with me," Isakson said.

Isakson also said he could be open to expanding background checks if done in a way that protects free access to guns and mental health privacy.

Later in the week, the Georgia lawmaker is coordinating a dinner with President Obama and 11 Republican colleagues, the latest in a White House charm offensive designed to win favor with the GOP. Isakson said he was encouraged by the outreach attempt, but that the "proof will be in the pudding" as lawmakers work to reach a budget deal.

"I don't know what to expect, except that I think more of our talk is going to be about [the] budget … about getting our arms around the biggest problem that faces our country," Isakson said. "That's what I hope it's about, that's what I believe it will be about."