But if they are on the same page, it would represent a remarkable change from the past few months. Here are some of the kumbaya claims they made Monday, with background on what we've actually seen lately.
The claim: “My relationship with this gentleman is outstanding, has been outstanding.” — Trump
The reality: McConnell's allies say that this fall, McConnell and Trump have settled into a productive relationship in which they talk frequently, especially about how to get a tax overhaul done. But Trump glossed over the fact that he was more or less at war with McConnell during the summer over who was to blame for failing to repeal or roll back Obamacare.
The two politicians' relationship deteriorated so much that Trump's supporters have called for McConnell to step down as majority leader. A few weeks ago, Vice President Pence's chief of staff, Nick Ayers, suggested to Republican donors that they “purge” GOP lawmakers who don't support the president's agenda.
And just an hour before lunching with McConnell, Trump basically endorsed former adviser Stephen K. Bannon's war on McConnell and the Republican establishment.
“It's a season of war on the GOP establishment,” Bannon said Saturday.
“I can understand fully how Steve Bannon feels,” Trump said Monday.
The claims: “Obama signed Obamacare in March of Year 2 [of his presidency]." — McConnell
“And we're nine months. So we could have a long way to go, but that's okay.” — Trump
The reality: Trump seems to be repeating one of McConnell's talking points, that passing major legislation takes time.
But this summer, when McConnell suggested Trump's expectations were out of whack, Trump made very clear he thought the Senate had more than enough time to get something done.
The claim: “I want to focus on tax cuts.” — Trump
The reality: This is an aspirational statement on the president's part, but it's not one he's lived up to so far.
Trump was notably absent from the health-care debate, a fact that McConnell's supporters on Capitol Hill say was a big reason a bill failed to get enough Republican support. Now that the Senate has moved on to tax legislation, Trump has taken up valuable time and headlines by feuding with the NFL and Sen. Bob Corker (R-Tenn.).
“Congress's de facto stance is gridlock,” Alex Conant, a GOP strategist and former aide to Sen. Marco Rubio (R-Fla.), told The Fix recently. “Without leadership, Congress does nothing.”
The claim: “Something that people aren't talking about his how many judges we had approved.” — Trump
The reality: Replace “people” in this sentence with “the president” and you'll get a more accurate statement. McConnell's allies say he is working hard to get the Senate to approve Trump's judicial and political nominees. But up until now, Trump hasn't publicly praised McConnell for it.
Is it a coincidence that the first time the president directs attention to McConnell's work is after having lunch with the majority leader?
The claim: “We're totally together on this agenda.” — McConnell
The reality: It depends what agenda they're talking about. On health care, some Republicans say Trump has yet to specifically outline exactly what it is that he wants. He celebrated House Republicans' version of a repeal in the Rose Garden, then later called it “mean.”
On immigration, Trump has switched his position on whether he wants to protect “dreamers” — younger immigrants who were brought to the country illegally as children — from deportations half a dozen times or so in the past month.
And on taxes, Trump and Republicans have yet to agree on details about just what their tax bill will do. They released a plan in September that contains broad outlines of tax cuts, but they have yet to agree on how they'll pay for it all.