Reading the docs of upquote package indicates that, for the standard CM fonts, a \ttfamily\char13 already produces the desired glyph, so I just made the ' active and redefined it.
EDITED so that straight quote is only active in the sftabbing environment, and restores to normal quote thereafter.
EDITED to include cmap package which allows proper cut/paste of quote character from PDF (see Can't copy-paste from my PDF. Any idea why?)
ADDENDUM added for those for whom cmap approach does not work.
\RequirePackage{cmap}
\documentclass{article}
\newenvironment{sftabbing}
{\par\sffamily\small\squoteon\tabbing}
{\endtabbing\squoteoff\par}
\let\svquote'
\catcode`'=\active
\def\squoteon{\catcode`'=\active%
\def'{\setbox0=\hbox{\ttfamily\char13}\raisebox{1pt}{\box0}}}
\def\squoteoff{\catcode`'=12\let\'\svquote}
\catcode`'=12
\begin{document}
\begin{sftabbing}
INSERT \= INTO Shippers(CompanyName, Phone) \\
\> VALUES ('Federal Express', '02 752 75 75') \\ \\
UPDATE \= Shippers \\
SET \> CompanyName='Fedex' \\
WHERE \> CompanyName='Federal Express' \\ \\
SELECT \> ProductID, ProductName \\
FROM \> Products P \\
WHERE \> EXISTS ( \\
\> SELECT \= * \\
\> FROM \> Orders O JOIN Customers C ON \\
\> \> O.CustomerID = C.CustomerID JOIN \\
\> \> OrderDetails D ON O.OrderID = D.OrderID \\
\> WHERE \> C.Country = 'Germany' AND D.ProductID = P.ProductID )
\end{sftabbing}
Test's of quote
\end{document}
Zoom:

For comparison, the straight quote activated by the textcomp package in \sffamily looks like a rectangular block, which may be more in keeping with the sf style, but which I find unattractive:

I thus chose to retain the \ttfamily look for the quote character.
ADDENDUM:
For those for whom the cmap package does not provide relief for the copy/paste feature from PDFs, an alternative "glyph-to-unicode" approach is here. Both methods work for me, but the OP was having difficulty with the cmap approach.
\documentclass{article}
\newenvironment{sftabbing}
{\par\sffamily\small\squoteon\tabbing}
{\endtabbing\squoteoff\par}
\let\svquote'
\catcode`'=\active
\def\squoteon{\catcode`'=\active%
\def'{\setbox0=\hbox{\ttfamily\char13}\raisebox{1pt}{\box0}}}
\def\squoteoff{\catcode`'=12\let\'\svquote}
\catcode`'=12
\pdfgentounicode=1 %
\input glyphtounicode.tex %
\begin{document}
\begin{sftabbing}
INSERT \= INTO Shippers(CompanyName, Phone) \\
\> VALUES ('Federal Express', '02 752 75 75') \\ \\
UPDATE \= Shippers \\
SET \> CompanyName='Fedex' \\
WHERE \> CompanyName='Federal Express' \\ \\
SELECT \> ProductID, ProductName \\
FROM \> Products P \\
WHERE \> EXISTS ( \\
\> SELECT \= * \\
\> FROM \> Orders O JOIN Customers C ON \\
\> \> O.CustomerID = C.CustomerID JOIN \\
\> \> OrderDetails D ON O.OrderID = D.OrderID \\
\> WHERE \> C.Country = 'Germany' AND D.ProductID = P.ProductID )
\end{sftabbing}
Test's of quote
\end{document}
\usepackage[T1]{fontenc}, this would be sufficient: using"would produce straight quotes. – egreg Apr 22 '14 at 15:33"for producing closing double quotes is wrong to begin with. See Why this one symbol"works as one double quote as well – egreg Apr 22 '14 at 16:02