Story highlights Iowa Sen. Chuck Grassley is putting together a new gun control bill

Grassley is skeptical of new background checks -- an issue at the heart of the debate

Grassley's bill could provide cover for red state Democrats and some Republicans

Obama urges Congress not to get "squishy" on gun control

A top congressional Republican is drafting alternative gun control legislation that threatens to undermine proposals now under consideration by leaders of the Senate's Democratic majority.

A spokeswoman for Iowa's Chuck Grassley refused to give CNN details of the senator's plan. In the past, however, he has backed measures to deter "straw purchases" to clamp down on gun trafficking. He also supports new safety provisions for schools.

Grassley is a staunch opponent of a ban on assault weapons and high capacity magazines. He has also expressed skepticism about new background checks -- an idea at the heart of the current congressional debate.

"Sen. Grassley is putting together a bill to reduce gun violence without violating the constitutional rights of law-abiding citizens," spokeswoman Beth Levine told CNN. "The bill is still being written, so we're not able to share it at this time."

The plan being put together by Grassley -- first reported by Politico -- further complicates the politics of gun control in Congress, where the National Rifle Association is extremely powerful.

President Barack Obama pushed new gun control legislation near the top of the legislative priority list in the wake of December's school massacre in Newtown, Connecticut, where 20 first-graders were killed. But Democrats are struggling to find the 60 votes needed to push any new measures through the 100-member Senate.

Alternative legislation from Grassley could provide cover for moderate Democrats from more conservative states looking to back some sort of bill not vehemently opposed by the NRA or other political heavyweights. It could also help firm up GOP opposition to more expansive legislation including background checks.

Addressing gun control supporters at a White House event on Thursday, Obama accused gun rights activists of playing a crass game of political obstruction.

"There are some powerful voices on the other side who are interested in running out the clock, or changing the subject," the president said. "Their assumption is that people will just forget about it" as Newtown recedes further into the past.

If that happens, said Obama, then "shame on us."

The list of proposals backed by the president in the aftermath of Newtown includes expanded background checks, tougher laws against gun trafficking and straw purchases, and improving safety at schools. Obama also supports a renewal of the assault weapons ban, though that provision has been virtually abandoned by Senate Majority Leader Harry Reid, D-Nevada.

The president on Thursday rejected arguments by opponents of the legislation that the measures under consideration by Democrats -- including background checks -- would strip Americans of their constitutional right to bear arms.

"What we're proposing is not radical. It's not taking away anyone's gun rights," Obama said. Congress shouldn't get "squishy because time has passed and maybe (the issue's) not on the news every day."

But much of what Obama considers "squishy" is seen by senators like Grassley as a principled defense of basic freedoms.

"Throughout history, governments have wanted to shut up those who would criticize government, to suppress unpopular religions, or to disarm people," Grassley declared at a January 30 Senate Judiciary Committee hearing.

"The Constitution for 225 years has established a government that is the servant of the people, not the master," he said. As "we consider and debate legislation arising (Newtown and other) tragedies, I hope that we will proceed with proper understanding of the relationship that the Constitution establishes between government power and individual liberty."