Criticizing Sonia Sotomayor could cost the GOP, some Democrats are hoping, as strategists see a political upside to the recent allegations by Newt Gingrich and Rush Limbaugh that Sotomayor is a racist and should withdraw her Supreme Court nomination.

The Democratic Congressional Campaign Committee (DCCC), for instance, is looking in particular to capitalize on Newt Gingrich's remark, via Twitter Wednesday, that "White man racist nominee would be forced to withdraw. Latina woman racist should also withdraw."

The DCCC sent a press release to the districts of its GOP 2010 targets Friday, asking if the GOP Reps. would repudiate Gingrich's statement and highlighting Gingrich's role in an upcoming fundraiser, to be held June 8, at which the GOP campaign committees are expected to take in millions.

The release asks:

With Gingrich soon to headline a lucrative fundraising dinner to benefit House Republicans like Representative [X], this begs the question -- will Representative [X] repudiate Gingrich's offensive remarks? Even Senator John Cornyn, a top Republican leader in the Senate, took the unusual step of criticizing Gingrich's overheated rhetoric. Now will Representative [X] follow suit?

The question seeks to put Republicans in a tough spot--and it's similar to the strategy Democrats employed earlier this year in asking Republicans whether they view Rush Limbaugh as their party's leader, and whether they, too, wanted President Obama to "fail."

Political insiders agree that opposing Sotomayor is a bad idea for the GOP, according to a National Journal poll released today--many warning it could cost to GOP support from Hispanics--and National Republican Senatorial Committee Chairman John Cornyn rebuffed the criticisms of Gingrich and Limbaughtoday, as the DCCC noted in its release.

With the June 8 fundraiser just over the horizon, one Democratic strategist told me Dems will use Gingrich's remark to put more pressure on Republicans as the date draws closer.

Democratic strategists see advantage in the Sotomayor criticisms leveled by Gingrich and Limbaugh, particularly as the GOP struggles to find its identity on the conservative-to-moderate spectrum and vie for Hispanic votes.

Sotomayor's nomination--and the attacks of Newt and Rush--"could present problems for a lot of Republicans, especially those in primaries," one strategist told me.

Notably, Florida Gov. Charlie Crist--whose Senate primary opponent, Marco Rubio, has attracted some conservative support--has yet to officially react to Sotomayor's nomination. The GOP gubernatorial primary in Texas, which pits Gov. Rick Perry against the more moderate Sen. Kay Bailey Hutchison, could also turn Sotomayor into a campaign issue.

"The Hispanic populations of a lot of states where these races are going to be...will be interesting," the same strategist pointed out. Opposing Sotomayor may help garner support among conservative GOP primary voters--but not among Hispanics in a general election.

For now, Democrats haven't unleashed a full-blown message strategy as Limbaugh's "fail" comment initiated--but there's a feeling among Democrats that Gingrich and Limbaugh, in opposing Sotomayor so forcefully with allegations of racism, have handed them an opportunity to cause trouble for their opponents.