Republican Sen. John Cornyn (Texas) is betting the White House is wishing GOP presidential candidate Jon Huntsman (R) would run for president as an Independent.

Cornyn, one of the GOP's campaign gurus who heads the National Republican Senatorial Committee (NRSC), mused on Twitter that it would be in President Obama's interest for Huntsman to seek the presidency as an Independent candidate.

Cornyn said on Twitter:

WH wishes “@CNN: CNN Opinion: Why John Huntsman should run as an independent:  http://t.co/ouFmsQV

Huntsman is a former governor of Utah, who left that position to serve a stint as Obama's ambassador to China. He then stepped down as ambassador to pursue the Republican presidential nomination.

In his bid for the GOP nod, Huntsman's sought to firmly stake out his space in the field as a more centrist alternative to candidates like Mitt Romney, the former Massachusetts governor, or Texas Gov. Rick Perry (R) and Rep. Michele Bachmann (R-Minn.), among others.

But Huntsman's had trouble getting traction in his pursuit of the presidency; two recent national polls in the last week showed him in the low single digits versus the other candidates for the nomination.

The CNN article to which Cornyn had linked was an opinion piece by LZ Granderson, who floated the idea of Huntsman as a third-party candidate.

Huntsman's made no mention of such a possibility, and appears to have his sights set only on the Republican nomination. Cornyn's tweet would seem to belie a concern, though, that a third-party bid by Huntsman would subtract more votes from the eventual Republican nominee than from Obama.