A Dictionary of English Phrases has an entry for 'Dame Partington's broom,' which redirects the reader to 'Mrs Partington':
Mrs. Partington: the personification of
impotent prejudice.
From a personage invented by Sydney Smith in a
speech at Taunton in 1831, who at a
time of storm and high tide took out
her mop in order to sweep away the
Atlantic.
Here is the original speech:
"I do not mean to be disrespectful but the attempt of the Lords to stop the progress of reform reminds me very forcibly of the great storm of Sidmouth and of the conduct of the excellent Mrs Partington on that occasion.
"In the winter of 1824, there set in a great flood upon that town - the tide rose to an incredible height - the waves rushed in upon the houses, and everything was threatened with destruction. In the midst of this sublime and terrible storm, Dame Partington, who lived upon the beach, was seen at the door of her house with mop and pattens, trundling her mop, squeezing out the sea water and vigorously punching away the Atlantic Ocean. The Atlantic was roused.
"Mrs Partington's spirit was up; but I need not tell you that the contest was unequal. The Atlantic Ocean beat Mrs Partington. She was excellent with a slop or a puddle, but she should not have meddled with a tempest."
I have no idea about the martyrs of Chicago.
For fun, here's the poem version:
DAME PARTINGTON stood on the shore,
As stern as old woman could be:
And her wonderful mop she bore,
With which to sweep back the sea.
Before her crept up the tide,
Behind her arose the towers
That rise in stately pride
Round Isis's mystic bowers :
To mask each yawning gap,
Where the rampart is crumbling down;
On her head was a trencher cap,
On her back was a Master's gown.
Proudly that gown she wore,
As one of her worth aware;
And her mop-handle bore
"Tests” carved in letters fair.
Now and anon she backed,
"High and dry," from reach of the brine,
To save her reticule, packed
With Articles Thirty-and-Nine,
In the which, as her ballast and stay,
And sheet-anchor she seemed to confide,
As in forcible-feeble way
She apostrophised the tide :
If it's coming-let it come,
DAME PARTINGTON is here!
Wild waves might frighten some :
DAME PARTINGTON knows no fear!
"These waves may rise and roar,
And with weaker bars make free;
But e'er they flood this shore,
They've to deal with my mop and me!"
(Not the whole thing, which is available here)