This is what I get from the link above. I think they made a few small changes (updates) to what was on the LP.

****************************************
Another Movie Star
(Songwriter ??)

(spoken)
Do you worry about Vietnam?
Do you fear the NATO split?
Do you dream about the national debt?
That doesn't help a bit!

Don't fear Red China's bomb threat.
Don't cry for the old UN.
Just remember that the Republicans
Are comin' back again.

(sung)
They know that what this country really needs is
Another movie star
No one else can steal those leads like
Another movie star

Ron Reagan is the governor
George Murphy in D.C.
Now to complete the picture
All we need is Sandra Dee

'Cause bonny Ronny Reagan knows experience pays
So California better get set for Death Valley Days

Won't it be great when we can say
All the Senate is a stage
Put politics where it belongs
On the amusement page

And though our next President may not have scored
In the Senate or Supreme Court or the Cabinet my Lord
Hey won't it be fun to know he won an Academy Award
Because the country needs another movie star.

(spoken)
Margaret Smith, you better chase
Tiny Tim's in the race

And over in France, won't it be groovy
Bardot as Premier, DeGaulle's in a movie!

Tuesday Weld, you'll make it, too
When Justice Douglas marries you

Even England's makin' the scene
Ringo's next in line for Queen

(sung)
Oh, gee, it's nice to see the GOP
With such a grand old plan
They may not have a leader any more, but
They've got a leading man

And now we'll be safe, for if someone slips
And the finger on that little old red button was tripped
Why, it simply wouldn't matter, folks, it wasn't in the script
That's why the country needs another movie star.

Now Lyndon is smarter
And Hubert's more clever
But the GOP knows
Movies are better than ever
So everybody sing
The stars and stars forever...

(spoken)
Well after all George Murphy danced his way into the Congress
And Ronald Reagan acted his way into a governorship
And George Hamilton...well, he did the best he could

(sung)
'Cause we need a movie
A groovy groovy movie
Hey don'tcha love a pretty movie star
*************************************

For what it's worth, I think Tom Lehrer's song about George Murphy was much better.