(CNN) If President Donald Trump is truly serious about his vow to come up with "solutions" to gun violence, he has a golden chance to show it this week.

Trump could march into the Conservative Political Action Conference, a bulwark of support for the Second Amendment, on Friday and explain why change is needed following the latest mass tragedy last week at Marjory Stoneman Douglas High School in Parkland, Florida.

The timing of the annual conservative jamboree is auspicious because it will offer Trump access to activists on the right, who he must win over to get anything significant done.

On Tuesday, facing rising political heat after the Parkland massacre, Trump, as he often does, blamed his predecessors for a lack of action and said he would be different, despite widespread skepticism among gun control activists about his sincerity and capacity to make the case for change.

"We're going to come up with solutions. It's been many, many years, and there have been no solutions. We're going to come up with solutions," Trump said at the White House.

For anything but the most limited measures -- for example, a push toward banning devices that boost the firing power of semiautomatic rifles, which he announced Tuesday -- Trump must offer cover to conservative lawmakers in primary races and mount a consistent push for compromise in Congress.

The President also called in a tweet for Democrats and Republicans to work to "strengthen" background checks -- though he gave no specifics, so it was unclear how far he was planning to go.

Any serious action will require the kind of leadership that could cause him to alienate parts of his political base, something that Trump has been reluctant to do in his first 13 months in office.

So far, he has been more keen to highlight the failure of the FBI to stop the Florida high school carnage and the need to fill loopholes in mental health care than to accept the case for changing firearms laws.

But as a Republican president, perhaps the most pro-firearm chief executive in American history, Trump is, in theory, in a unique position to use his good standing with Second Amendment activists to make the case for gun reforms.

In his appearance at CPAC last year, for instance, he poured praise on Wayne LaPierre, executive vice president of the National Rifle Association, who is expected to again attend the event, outside Washington, this year.

"They're great people. And by the way, they love our country. They love our country. The NRA has been a great supporter. They love our country," Trump said in 2017.

But gun control advocates doubt that Trump really means what he says, after he ran for office warning that his opponent, Hillary Clinton, would remove the constitutional right to bear arms and he rode into the White House with the firm backing of the NRA, which opposes most attempts at real change.

Growing public demands for action on guns

If Trump does decide to take a risk and lead the charge on an issue that would require tough votes by conservative lawmakers -- perhaps on strengthening background checks for gun purchases -- it would be a departure for his presidency

In recent weeks, for instance, on another issue germane to his appeal to his base -- immigration -- the White House was unwilling to irritate the base and worked to scuttle a bipartisan Senate compromise that would have shielded hundreds of thousands of people who had been brought to the US illegally as kids in return for border wall funding.

But Trump needs to do more than protect his right flank.

Political pressure on the White House is quickly intensifying as the activism of Florida students begins to morph into a nationwide "never again" movement.

"President Trump, I think that it is really important that you listen to us because we are your constituents, you are working for us and kids are dead," Sofie Whitney, a survivor of last week's shooting, said on CNN's "The Lead" with Jake Tapper.

"You are avoiding us. I'd like to talk to you."

JUST WATCHED FL school shooting survivor reacts to Trump action on bump stocks Replay More Videos ... MUST WATCH FL school shooting survivor reacts to Trump action on bump stocks 03:49

Whitney spoke from a bus as she traveled with fellow students to lobby state lawmakers in Tallahassee, Florida, and as a new Quinnipiac University poll found growing support for reforms.

In the survey, 66% of Americans called for stricter gun laws, an idea supported by gun owners 50% to 44%.

Still, lawmakers have ignored the totality of national opinion in the past in deference to opinion in their districts and the power of the NRA in primary and state races. And Trump has often played into the powerful gun lobby group's conceit that any reform of gun laws is a slippery slope that will inevitably lead to the total withdrawal of the right to bear arms.

But in a sign the pressure is beginning to tell in Washington, Trump announced on Tuesday that he had ordered the Justice Department to propose a rule to ban bump fire stocks, the device that allowed the gunman at the Las Vegas massacre in October to fire on concertgoers more rapidly, mimicking automatic weapons fire.

White House press secretary Sarah Sanders told reporters that the President also did not rule out raising the legal age at which someone could buy an AR-15 style weapon, the type of firearm used by the 19-year-old confessed shooter in Florida.

The move on bump stocks was hardly a major step by Trump -- he had raised the possibility of such action after the Las Vegas shootings but never made a concerted public push for it until Tuesday.

It's an open question whether he would have moved had the Florida tragedy not happened. The measure also would have done nothing to stop the killing spree of the Florida gunman last week. And gun rights advocates immediately argued that only legislation could outlaw the use of bump stocks.

"Donald Trump is trying to escape blame by playing catchup with our kids' safety," said Peter Ambler, executive director of Giffords, the gun violence reform operation set up by former Rep. Gabby Giffords, an Arizona Democrat who was shot in the head and severely wounded in 2011.

"A real leader would have gotten Congress to pass a ban on bump stocks after the horror of Las Vegas, the worst mass shooting in modern American history," Ambler said. "But the president is proposing too little too late."

Andrew Patrick, media director of the Coalition to Stop Gun Violence, questioned whether Trump was looking for a face saver with his announcement.

"Until the President calls for a vote on bump stocks and passage in Congress and says that he will sign it, things like this are just thoughts and prayers in memorandum form," he said.

Huge obstacles to reform

The political obstacles to real action to stop the spate of mass shootings in America remain significant.

Even though the Quinnipiac poll found that 97% of Americans support universal background checks, the momentum after gun massacres has a way of waning in subsequent weeks.

In a sign that tragedy often does not move the polarized debate over guns in society, Florida's House of Representatives voted Tuesday to kill a bill banning AR-15 rifles, assault weapons and large capacity magazines.

In 2012, with the nation traumatized in the wake of the massacre at Sandy Hook Elementary School in Newtown, Connecticut, President Barack Obama sat where Trump does now and launched a major push for gun control.

In the end, however, even a watered-down measure that would have tightened background checks failed to get to a final vote in the Senate amid opposition from Republicans and Democrats in conservative states.

Obama fumed at the failure to act and said years later , "This is a political choice that we make to allow this to happen every few months in America. We collectively are answerable to those families who lose their loved ones because of our inaction."

That is the dilemma that Trump faces right now. The question is how long will momentum for action dominate Washington politics -- and how far is the President truly prepared to go while taking his party with him?