The last few weeks have not been kind to Donald Trump, and the numbers are starting to show it.

The presumptive GOP nominee has fallen behind Hillary Clinton, the presumptive Democratic nominee, in national and swing state polls. And causing even more concern for Trump fans, a Federal Election Commission report earlier this week showed him with far less cash on hand than Clinton's campaign, reflecting a fundraising operation in sore need of expansion, at best.

Still, it's not always the case that the candidate with the most money or the best early standing in polls emerges the victor. Narratives, external events, even policy proposals can all shape the outcome of an election. But the nuts and bolts of campaigning, the numbers and fundamentals undergirding the contest, have historically mattered quite a bit. And at this moment, as the general election begins, they don't look good for Republican hopes of capturing the White House.

New polls

Trump pulled almost even with Clinton in national polls in the weeks after he effectively secured the Republican nomination at the beginning of May. But his standing has since eroded - he's trailed Clinton in every major national poll released in the four weeks, and some new surveys released this week point to a steady Clinton lead.

An Economist/YouGov poll released Wednesday showed Clinton up four points over Trump, 43 to 39 percent. A Reuters/Ipsos tracking poll released Tuesday found Clinton ahead by nine points, 44.5 to 35.5 percent. A CNN/ORC poll released Tuesday found Clinton up by five, 47 to 42 percent. A CNBC poll released Monday found Clinton up by the same margin, 40 to 35 percent. And a Monmouth poll from the same day found Clinton with an eight-point lead, 49 to 41 percent.

Several swing state surveys also show Trump falling behind, though he remains in a competitive position in some key Midwestern battleground states.

New Quinnipiac polls out of Florida, Ohio, and Pennsylvania released Tuesday showed Trump slipping in two of the three crucial swing states but holding steady in the third. He's now eight points behind Clinton in Florida, 47 to 39, according to Quinnipiac, slipping from the one-point deficit he held last month in the same poll. In Ohio, Quinnipiac now finds Trump even with Clinton at 40 percent each, but he was four points ahead last month. In Pennsylvania, the results have scarcely changed: Trump is now one point behind Clinton, 42 to 41 percent, the same margin as last month.

And Marquette University poll last week found Trump down nine points, 46 to 37 percent, in Wisconsin - another Midwestern state with a lot of white, working-class voters that Trump hopes he can lure into the GOP fold by November.

Fundraising and organization

Of course, poll numbers can and do change. But one way campaigns can swing survey data in their favor is by committing resources - personnel and money - to the problem. And by those metrics, as well, Trump trails his Democratic rival.

Trump's campaign began June with only $1.3 million cash-on-hand - a far cry from the over $42 million Clinton had stockpiled. And super PACs supporting Trump and Clinton reflected a similar cash gap: the main pro-Clinton outfit had $52 million on hand at the end of May, while the largest pro-Trump group had only $500,000.

Trump's campaign, moreover, pulled in only $3.1 million in private donations in May, while Clinton netted roughly $26 million.

Worth noting: Trump's cash-on-hand numbers at the end of each month have reflected the extent of his self-funding and the limited fundraising to this point. He's been loaning money to his campaign only as needed. Here's a look at where his campaign's war chest stood at various points throughout the election:

June 30, 2015: $488k on hand

September 31, 2015: $255k on hand

December 31, 2015: $6.97m on hand

January 31, 2016: $1.58m on hand

February 29, 2016: $1.34m on hand

March 31, 2016: $2.11m on hand

April 30, 2016: $2.41m on hand

May 31, 2016: $1.29m on hand

Next month's FEC filings, which are due July 20 and will cover the full month of June, could provide a clearer read on the state of Trump's finances, particularly on the question of whether he'll have success raising money from outside donors. But given reports of reticence in the GOP donor class, it's possible fundraising worries will continue to nag his bid to some degree.

Trump largely self-funded his primary effort and is open to doing the same in the general election.

The effects of Trump's current money deficit can be seen in his campaign's paltry organizing and advertising presence. His campaign estimated earlier this week that it has about 30 paid staffers on the ground across the country, according to the Associated Press, while Clinton has deployed over 700 staffers. And on the airwaves, Clinton is also dominant: Her campaign is plowing $23 million into advertising in eight battleground states over the next several weeks, while Trump's campaign hasn't spent a dime.

Trump claims that he doesn't need to spend money to be successful. He believes the success of his unorthodox primary campaign shows he can rely largely on earned media, rather than paid media, to get his message out. And he's hoping to farm out many of the infrastructural and organizational tasks typically performed by a campaign to the Republican National Committee and other party organs.

It's a gutsy bet. We'll have to wait for November to see whether it was a wise one.

Tune into "Face the Nation" on Sunday for the latest news and analysis on the 2016 election. Check your local listings for airtimes.

CBS News Senior Political Editor Steve Chaggaris contributed to this report.