WASHINGTON -- Sens. Dianne Feinstein and Lindsey Graham called Tuesday for an end to hyper-partisanship, saying the urgent issues the nation faces require lawmakers on Capitol Hill to focus on solving problems instead of assigning blame.

Feinstein, a California Democrat, and Graham, a South Carolina Republican, expressed great respect for each other as each accepted the Prize for Civility in Public Life from Allegheny College at a National Press Club ceremony.

The senators are at the forefront of two of the most contentious issues before Congress. Feinstein is pushing a renewal of the assault weapons ban that lapsed in 2004, while Graham is helping to lead an effort to change immigration law.

"We're entering into a time of problem-solving simply because we're running out of time not to solve our problems as a country," Graham said. "So I think it's our turn to shine."

Feinstein and Graham said they could count on getting a fair hearing from each other even when they disagreed on policies.

"We've got the immigration issue. We've got the sequester issue," Feinstein said, referring to looming forced cuts in federal spending. "I truly believe that Lindsey and I could sit down and work out solutions to both issues if we were able to do that. But we're not. We've got polarization up and down our ranks."

After the ceremony, Graham offered an example of a trademark willingness to compromise as he tried to help break the partisan impasse over the forced spending cuts that are slated to start Friday.

Graham said he'd be open to considering increased taxes if Democrats would weigh changes to Medicare and Social Security that would save expenses. "I'll raise revenue. Will you reform entitlements?" Graham told CNN in challenging President Barack Obama and allied congressional Democrats to cut a deal. "And together, we'll set aside sequestration in a way that won't disrupt the economy and hurt the Defense Department."

At the award ceremony, Feinstein offered a moving portrayal of how, as the chair of the San Francisco Board of Supervisors, she unexpectedly became the city's mayor in 1978, describing how she found the body of county supervisor Harvey Milk, the first openly gay elected official, moments after he and Mayor George Moscone were shot to death by a political rival.

"I became mayor as a product of assassination, a product of incivility, a product of violence," Feinstein said. "I think words matter. I think people are fragile. I think civility has an antithesis, and that antithesis is violence."

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