Story highlights The Senate push comes after President Barack Obama urged a congressional response

"There must be a groundswell of urgency from Americans pushing their elected officials," Oregon Sen. Ron Wyden said

Washington (CNN) Frustrated Senate Democrats conceded Thursday that even in the aftermath of several mass shootings, they don't have enough votes right now to push through gun control legislation. So they will try to build grassroots support by urging Americans to insist the Republican-controlled Congress act.

"There must be a groundswell of urgency from Americans pushing their elected officials," implored Sen. Ron Wyden of Oregon, where nine people were shot to death last week at a community college.

At a news conference on the Capitol steps, Democratic senators from states where mass shootings killed dozens of people outlined three "principles of action" they want adopted to curb gun violence. Those ideas center on improving background checks and curbing illegal gun sales to keep weapons from the many unstable people behind these shootings.

"The roll call of American gun tragedies is already far, far too long," said Wyden before reading off a list of afflicted communities, including Roseburg, Oregon, site of last week's shooting. "The victims and their families deserve better than a Congress that shrugs its shoulders and waits for the next tragedy."

The Senate push comes after President Barack Obama, exasperated by the shootings during his years in the White House, urged a congressional response

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