President Obama moved Thursday to put the muscle of the White House and his network of supporters behind a gun control package tracking toward the Senate floor, calling on voters to pressure Congress into backing it as the proposal runs into resistance on Capitol Hill.

The president, in a set of brief remarks from the White House Thursday surrounded by the mothers of shooting victims, raised concern that the shock from the Newtown elementary school shooting could soon fade.

"Less than 100 days ago that happened. ... Shame on us if we've forgotten," Obama said. "I haven't forgotten those kids. Shame on us if we've forgotten."

Amid signals from Washington that the Senate bill could be losing momentum and high-dollar ad campaigns on both sides, the president was there to deliver a message to wavering lawmakers. "Don't get squishy," he said.

Obama, accusing opponents of drumming up "fear," urged supporters to call members of Congress and pressure them into backing the package.

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Republican Sen. Mike Lee, of Utah, ripped the president for the remarks, suggesting he was exploiting the Newtown tragedy.

"The proposals the president is calling for Congress to pass would primarily serve to reduce the constitutionally protected rights of law-abiding citizens while having little or no effect on violent crime," Lee said in a statement. "It is deeply unfortunate that he continues to use the tragedy at Newtown as a backdrop for pushing legislation that would have done nothing to prevent that horrible crime."

Lee said he and his conservative colleagues plan to ensure that any of the firearms proposals require a 60-vote threshold in order to proceed. This could be a high hurdle for the Senate to clear.

Already, Senate Majority Leader Harry Reid dropped from the main package a proposal to renew and expand the expired assault weapons ban.

The base bill will instead cover universal background checks, strengthened punishments for illegal trafficking and more money for school security.

Items like school security enjoy broad support. But the move to include private sales -- including gun show purchases -- in the background check system remains controversial in some circles. Plus the assault weapons ban, which Republicans most adamantly oppose, is still expected to get a vote as an amendment to the main bill.

The National Rifle Association, during and after Obama's remarks, tweeted a flurry of comments criticizing the latest Obama push. The group accused him of campaigning "against guns to please the fringe."

Both sides of the gun debate are stepping up their effort to sway Congress. While the NRA has been vocal since the start of the process, New York Mayor Michael Bloomberg just launched a $12 million ad buy in support of the legislation.

"It's not done until it's done," Obama said Thursday. "There are some powerful voices on the other side that are interested in running out the clock, or changing the subject. ... They're doing everything they can to make all our progress collapse under the weight of fear and frustration."