Sen. Ted Cruz's father immigrated to the United States from Cuba. (Justin Sullivan/Getty Images) Sen. Ted Cruz (R-Texas). (Justin Sullivan/Getty Images)

The Club For Growth stood with Sen. Ted Cruz (R-Tex.) Tuesday, calling for senators to vote against cloture on a stopgap spending bill that passed the House last week. The conservative, anti-tax group said it would it include the vote on its 2013 scorecard.

"To keep the House defund language secure, and to continue using the leverage of the continuing resolution, opponents of ObamaCare should vote "NO" on the cloture vote to end debate," wrote the group's vice president of government affairs Andy Roth in a note to congressional offices.

Cruz has been urging his colleagues to vote against cloture on the bill that keeps the government running and defunds Obamacare, even though the measure is exactly what he's long demanded.

Why? Because he wants to prevent Majority Leader Harry Reid (D-Nev.) from stripping out the defund provision and passing a new continuing resolution that restores funding for the health-care law with a simple majority. Under Senate rules, Reid can do that.

Cruz has failed to win the support of high-ranking Republicans for his plan. On Monday, Senate Minority Leader Mitch McConnell (R-Ky.) and Minority Whip John Cornyn (R-Tex.) both said they won't seek to block the bill. Sen. Roy Blunt (R-Mo.) joined them Tuesday.