Senate Republicans must "stand our ground" against their Democratic counterparts in next week's federal spending showdown over ObamaCare, Sen. Ted CruzTed CruzGOP wrestles with soaring deductibles in healthcare bill Cruz: Tax reform chances ‘drop significantly’ if healthcare fails Ex-CBO directors defend against GOP attacks on ObamaCare analysis MORE (R-Texas) said Sunday.  

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House Republicans scored a "tremendous victory" on Friday, Cruz said, when GOP members approved legislation to defund ObamaCare, as part of a plan to avoid a government shutdown in October.

"It is now our turn to unify our stand with [House] Republicans," Cruz said during an interview on "Fox News Sunday."

"I think we should stand our ground" against ObamaCare," he added.

Cruz has drawn harsh criticism from rank-and-file House Republicans, who accused the likely presidential hopeful of picking a political fight with Senate Democrats he will more than likely lose.

The rift highlights the desire by GOP lawmakers to avoid blame for any shutdown that occurs because of demands to kill ObamaCare.

Sen. Claire McCaskillClaire McCaskillFederal Election Commission must not shy away from Russia probe Senate Dems warn potential Missouri GOP recruit with opposition research dump GOP rep declines Senate bid challenging McCaskill MORE (D-Mo.) said Cruz's political play in the Senate is more about the looming 2016 presidential race than it is about preventing a government shutdown.

Lawmakers should not "throw tantrums when we lose elections," McCaskill said Sunday, regarding repeated House GOP efforts to kill ObamaCare.

"This is about running for president for Ted Cruz," not a desire to stave off a potentially devastating shutdown, she added during an interview with Fox News.

Cruz declined to respond to McCaskill's comments but did accuse Senate Majority Leader Harry ReidHarry ReidConservative Senate candidate calls on GOP to end filibuster Ex-Reid aide: McConnell's 'original sin' was casting ObamaCare as 'partisan, socialist takeover' GOP faces growing demographic nightmare in West MORE (D-Nev.) of using "brute political power" to derail the House measure in the upper chamber.

Senate Republicans on Monday will begin eyeing amendments and a possible cloture vote to the Senate version of legislation to avoid a government shutdown, Cruz said.

If Republicans fail to push the House version of the bill through the Senate, Cruz reiterated his support on Sunday for a military-only funding measure in the House.