WASHINGTON (AP) — President Barack Obama’s sweeping gun-control package faces an uncertain future on Capitol Hill, where majority House Republicans are rejecting his proposals while the president’s allies in the Democratic-controlled Senate are stopping well short of pledging immediate action.

The fate of his plan could ultimately hinge on a handful of moderate Democratic senators. Although they are unlikely to endorse the president’s call for banning assault weapons, they might go along with other proposals, such as requiring universal background checks on gun purchases.

Several of these senators responded warily after Obama unveiled his proposals Wednesday with the challenge that “Congress must act soon.”

“I will look closely at all proposals on the table, but we must use common sense and respect our Constitution,” said Sen. Jon Tester, D-Mont. Tester told the Missoulian newspaper in his home state recently that he supports background checks but doesn’t think an assault weapons ban would have stopped the shootings at an elementary school in Newtown, Conn., where a gunman massacred 20 children and six adults before turning the gun on himself.

Obama’s proposals came a month after the shootings in Newtown, which he has called the worst day of his presidency. His announcements capped a swift and wide-ranging effort, led by Vice President Joe Biden, to respond to the deaths.

The $500 million plan marks the most comprehensive effort to tighten gun laws in nearly two decades. It also sets up a tough political fight with Congress as Obama starts his second term needing Republican support to meet three looming fiscal deadlines and pass comprehensive immigration reform.

The White House strategy for pressing Congress centers on building public support for the president’s measures.

“There’s only one voice powerful enough to make this happen: yours,” Obama wrote in an op-ed Thursday in The Connecticut Post.

The president is also expected to travel around the county pitching for his proposals and could activate his still-operational campaign organization, Organizing for America, to fight for the plan as well.

Campaign manager Jim Messina sent an email to Obama supporters Thursday urging them to sign a petition backing the president’s proposals and promising “more soon” from the organization.

Obama, seeking to sidestep some congressional opposition, also signed 23 executive actions Wednesday, including orders to make more federal data available for background checks and end a freeze on government research on gun violence. But he acknowledged that the steps he took on his own would have less impact than the broad measures requiring approval from Capitol Hill. He is also calling for limiting ammunition magazines to 10 rounds or less.

“To make a real and lasting difference, Congress, too, must act,” Obama said.

The question now is how and whether that happens.

House GOP leaders have made clear they’ll wait for the Senate to act first, since they see no need to move on the contentious topic if it doesn’t. “House committees of jurisdiction will review these recommendations. And if the Senate passes a bill, we will also take a look at that,” said Michael Steel, spokesman to House Speaker John Boehner.

Many rank-and-file Republicans scorched Obama’s proposal. “The right to bear arms is a right, despite President Obama’s disdain for the Second Amendment,” said Rep. Tim Huelskamp, R-Kan.

Senators are expected to begin discussions on how to proceed when they return to Washington next week from a congressional recess, according to a Democratic leadership aide who requested anonymity to discuss internal deliberations. They could end up breaking the president’s proposals into individual pieces, with votes possibly starting next month.

The argument went trans-Atlantic Thursday when Defense Secretary Leon Panetta, who is leaving the administration, talked to U.S. troops in Europe.

“Who the hell needs armor-piercing bullets except you guys in battle?” Panetta told the soldiers at the U.S. Army Garrison Vicenza in northern Italy. “For the life of me, I don’t know why the hell people have to have assault weapons.”

Panetta, who said he believes in the Second Amendment and has been a longtime duck hunter, was asked about the issue by a soldier who wanted to know what steps the Obama administration was going to take to deal with attacks in schools that “don’t have to do with tearing apart our Second Amendment.”

Known for his often blunt and colorful language, Panetta added that things can be done to protect children “so that the nuts that are out there won’t use these kinds of weapons to wipe them out.”

While the assault weapons ban is seen as having little if any chance of passage, support may coalesce behind requiring universal background checks, which is a top priority for advocacy groups that see it as the most important step to curbing gun crimes. The Brady Campaign to Prevent Gun Violence says 40 percent of gun sales are conducted with no criminal background checks, such as in some instances at gun shows or by private sellers over the Internet. Obama would seek to require checks for all sales.

Sen. Chuck Schumer, D-N.Y., already has sponsored a bill to require universal background checks that the Senate could take up, while Sen. Frank Lautenberg, D-N.J., has legislation banning ammunition magazines with more than 10 rounds.

Senate Majority Leader Harry Reid, D-Nev., a gun-rights backer who’s been supported by the National Rifle Association in the past, responded cautiously, saying he was committed to ensuring the Senate considers legislation on gun violence early this year. He didn’t endorse any of Obama’s proposals.

Despite the uncertainty on Capitol Hill and opposition from the powerful NRA, outside groups are encouraged by polling showing public support for changes to the law. They intend to try to harness that sentiment to pressure lawmakers.

A lopsided 84 percent of Americans back broader background checks, according to a new Associated Press-GfK poll. Nearly 6 in 10 Americans want stricter gun laws, the same poll showed, with majorities favoring a nationwide ban on military-style weapons.

“Now it’s up to us,” said Dan Gross, president of the Brady Campaign. He said his group would be working “to bring that voice to bear in this process, because without that it’s not going to happen.”