Cruz and Sens. Marco RubioMarco Antonio RubioHillicon Valley: Supreme Court takes up Apple case | Senate votes to block ZTE deal | Officials testify on Clinton probe report | Russia's threat to undersea cables | Trump tells Pentagon to create 'space force' | FCC begins T-Mobile, Sprint deal review Feehery: Betting on Trump Senate votes to block Trump's ZTE deal MORE (R-Fla.) and Mike LeeMichael (Mike) Shumway LeeTrump plan to claw back billion in spending in peril Senate passes 6B defense bill This week: House GOP caught in immigration limbo MORE (R-Utah) are urging their Republican colleagues to reject any federal spending plan that funds ObamaCare, risking a government shutdown this fall. They say it's the best opportunity the party has to stop the law before more provisions are implemented in 2014.

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Republicans have argued that healthcare mandates within the law will raise insurance costs for individuals and that employers who would have to provide insurance to full-time employees will reduce workers’ hours and stop hiring.

Cruz said Obama has broken “many promises” he made about how the law would be implemented.

“ 'If you like your plan, you can keep your plan.’ That was one of the many promises that President Obama made about his health care law,” Cruz said. “And it’s just not true.”

Cruz cited a Congressional Budget Office report that said 7 million people would lose their employer-sponsored insurance because those plans don't meet new coverage requirements.

Democrats point out that the law is already benefiting those with preexisting conditions who can’t be denied coverage, people younger than 26 who can stay on their parent’s insurance plan and women who now pay less for preventative healthcare.