His comments come as the Senate prepares to consider a House bill that would prevent the government shutdown, slated for Oct. 1, but defund Obamacare.
The House passed the bill Friday.
"Next week is a time for party unity. I think next week, all Senate Republicans, I hope, should come together and support the House bill," Cruz said on Fox News Sunday.
Cruz said he is willing to filibuster if Democrats insert funding for the healthcare law into the bill.
"If the majority is going to run over the minority with a train, the minority has the ability to stop them," he said.
Cruz argued that the American people are against Obamacare, and that, as a result, the elected representatives should listen to their constituents and approve the House bill.
"American people are hurting because Obamacare isn't working. It's killing jobs, it's driving up their health insurance rates, it's causing them to be pushed in to part-time work. It's causing them to lose their insurance," he said.