(CNN) - President Donald Trump claimed Tuesday that many Republicans support his push for strengthening background checks on gun sales -- a view that appears at odds with what lawmakers are telling the President in private even as he presses for action.
It's a sign of a possible divide between Trump and his party as long as the President maintains his position that background checks are a necessary response to two mass shootings earlier this month.
He upheld that view in conversations with advisers over the weekend as he began a weeklong working vacation in New Jersey, according to people familiar with the matter. Trump has said he believes he needs to take a concrete step on gun control, rather than symbolic. He's been encouraged by some aides, including daughter Ivanka, to press on background checks.
But others -- including those with more experience dealing with Washington Republicans -- have appeared skeptical. There isn't evidence yet that Trump is wielding an aggressive arm-twisting campaign for a specific piece of legislation as the Senate continues its extended vacation. And an ever-nearing reelection campaign, when support from a gun-loving base will be essential, is likely to weigh on Trump's thinking.
Before boarding Air Force One in New Jersey, Trump said he has spoken with Sen. Mitch McConnell and claimed the Republican majority leader is on board with strengthening background checks. He added that lots of Republicans are.
"I am convinced that Mitch wants to do something," Trump said, even though McConnell's aides have made clear he hasn't endorsed any legislation related to gun control. "He wants to do background checks. I do, too. I think a lot of Republicans do."
Trump said he had also spoken with Democratic Sen. Chris Murphy of Connecticut -- an ardent supporter of gun control laws -- and thought it would be Democrats who prevented the passage of legislation on "meaningful background checks," though it's Democrats who have publicly called on Senate Republicans to take action in wake of the last two mass shootings.
"I don't know, frankly, that the Democrats will get us there," Trump said.
Private GOP opposition
Despite Trump's claims, several conservative allies and Republican lawmakers have privately voiced opposition to his push for background checks, claiming they wouldn't have stopped the shootings in Dayton and El Paso. These officials have tried to relay their concerns to Trump, encouraging him to advocate for so-called "red flag" laws instead, but he has not been receptive, they said.
Meanwhile, others close to the President have questioned how long his interest in and commitment to passing background checks will last. In the past -- including after the Parkland, Florida, high school shooting -- Trump has voiced strong support for strengthening checks on firearm purchases. But over time that stance softened as Republicans and the National Rifle Association made their opposition known.
Some in the White House are seeking to harness the President's current focus, including his daughter Ivanka, who has phoned some members of Congress to discuss various aspects of the gun control debate, one White House official told CNN.
"She has trusted relationships on both sides of the aisle and she is working in concert with the White House policy and legislative teams," the official said.
Others, however, are impressing on Trump a more dubious view. On Friday, as Trump flew to the Hamptons to attend a pair of fundraisers, he was joined by Republican Sen. Lindsey Graham, a chief proponent of the red flag laws, who said he would attempt to explain to Trump that background check measures -- including a bipartisan measure sponsored by Sens. Pat Toomey and Joe Manchin -- have failed previously because Republicans couldn't support them.
"We've all voted against the bill before," Graham said. "I'm trying to find some middle ground here."
Speaking on local radio last week, McConnell said he would not call the Senate back during its August break to vote on gun control measures -- a step Trump also said was unnecessary.
McConnell -- who is spending the recess nursing a shoulder injury at home in Kentucky -- acknowledged that red flag laws and background checks, in particular the Toomey-Manchin bill, would be central in gun discussions when the Senate returns from its summer recess in early September.
But he stopped short of supporting that bill. And he wouldn't even say whether either of those measures would be allowed to come to the floor for a vote.
"Those are two items that for sure will be front and center as we see what we can come together on and pass," he said.
Other Republicans have appeared more skeptical.
Republican Sen. Mike Rounds -- who gaveled in Tuesday's pro forma session in the Senate -- pushed back on the President's claims that Republicans support his push for strengthening background checks.
"The key is meaningful, and we haven't seen that," he told reporters, adding later: "There's a reason why a lot of this stuff has not been done already, and that's because it's not as easy as what it sounds like."
"I don't expect that things have changed much," said Sen. John Barrasso of Wyoming when asked whether the Republican caucus in the Senate has moved much on expanded background checks since the Manchin-Toomey bill failed in 2013.
Trump also finds himself at odds with the NRA, a group he fostered close ties with that has been clear in its opposition to expanding background checks. Last week, Trump held multiple conversations with Wayne LaPierre, the organization's chief executive, seeking to gauge the group's willingness to change its position.
But even as Trump has privately questioned the group's remaining influence amid internal upheaval, he found little wiggle room.
"The NRA opposes any legislation that unfairly infringes upon the rights of law-abiding citizens," LaPierre said last week. "The inconvenient truth is this: The proposals being discussed by many would not have prevented the horrific tragedies in El Paso and Dayton."
Democrats, meanwhile, have sought to keep the attention on guns as other issues -- including China trade developments and unrest in Hong Kong -- appear to be consuming more oxygen.
Senate Minority Leader Chuck Schumer said Tuesday that he was planning to ask the Trump administration to withdraw its request for $5 billion in border wall funding to redirect the money toward countering gun violence and white supremacy extremism.
And House Majority Leader Steny Hoyer held a news conference Tuesday along with some other House Democrats and activists urging McConnell to take up House-passed legislation to expand background checks, which the President has threatened to veto.
"He doesn't have to vote for it," Hoyer said of McConnell. "Every senator will have to make their own decision. But not to bring it to the floor is an abdication of his responsibility to the American people."
CNN's Jim Acosta contributed to this report.