Is it possible to refactor this extension method?

No, you can't do this. It would be nice, but it's not possible without some sort of AOP getting involved. I'm sure PostSharp can do a nice job, hopefully using attributes, and in Code Contracts it would just be:

Contract.Requires(qwerty != null);

Ideally I'd like a PostSharp attribute which generates the Code Contracts call - and I'll play around with that at some point - but until then, the extension method you've got is the best approach I've found...

(If I ever try the PostSharp + Code Contracts approach, I'll certainly blog about it, btw... Mono Cecil might make it reasonably easy too.)

EDIT: To expand on Laurent's answer, you could potentially have:

new { qwerty }.CheckNotNull();

And if you had lots of non-nullable parameters, you could have:

new { qwerty, uiop, asdfg }.CheckNotNull();

This would have to use reflection to work out the properties. There are ways that you could avoid doing the reflection on every access, building a delegate for each property and generally making it whizzy. I may investigate this for a blog post... but it's somewhat icky, and I prefer the idea of being able to just attribute the parameters...

EDIT: Code implemented, and blog post duly made. Ick, but fun.

In a word: no.

The extension method is passed a value. It has no idea where the value comes from or what identifier the caller may have choosen to refer to it as.

I find it easiest to do this using a code snippet.

In your example, I can type tna<tab>qwerty<enter>.

Here is the snippet:

<?xml version="1.0" encoding="utf-8" ?>
<CodeSnippets  xmlns="http://schemas.microsoft.com/VisualStudio/2005/CodeSnippet">
    <CodeSnippet Format="1.0.0">
        <Header>
                <Title>Check for null arguments</Title>
                <Shortcut>tna</Shortcut>
                <Description>Code snippet for throw new ArgumentNullException</Description>
                <Author>SLaks</Author>
                <SnippetTypes>
                        <SnippetType>Expansion</SnippetType>
                        <SnippetType>SurroundsWith</SnippetType>
                </SnippetTypes>
        </Header>
        <Snippet>
                <Declarations>
                        <Literal>
                                <ID>Parameter</ID>
                                <ToolTip>Paremeter to check for null</ToolTip>
                                <Default>value</Default>
                        </Literal>
                </Declarations>
                <Code Language="csharp"><![CDATA[if ($Parameter$ == null) throw new ArgumentNullException("$Parameter$");
        $end$]]>
                </Code>
        </Snippet>
    </CodeSnippet>
</CodeSnippets>