Asked about the year ahead on a press call with local reporters, Texas' senior senator, John Cornyn, who serves as the second-ranking Senate Republican, listed infrastructure and immigration bill among the next priorities. He said Democrats should be motivated to work with Republicans in the coming year, since 10 Democratic seats are up this year in states President Donald Trump won in 2016.
"I'm optimistic that we pick up some Senate seats in 2018, particularly if (Democrats) play politics and don't engage in some bipartisan governance," said Cornyn.
Trump went further in his State of the Union Address last month, saying he was "extending an open hand to work with members of both parties -- Democrats and Republicans." He called for their help on an immigration bill and said his White House had been meeting with both parties regularly.
Cruz, meanwhile, wants Republican to act on their own.
Last fall he introduced a tax plan that would rely only on Republican votes, while Trump was talking about working with Democrats.
The eventual tax bill different greatly from Cruz's plan, but no Democrats voted for its passage.
"I've been urging using more and more tools that can pass things on 51 (votes) because ... I can't go home to Texans and say, 'Well gosh, Democrats are opposing everything so we're going to do nothing,'" Cruz said Wednesday.
Among those tools, Cruz listed the Congressional Review Act, which allows Congress to vote to strike down rules made by the White House within a short span of time after their creation.
He also pointed to a legislative procedure called reconciliation, which allows lawmakers to pass legislation with a simple majority if it's related to the budget. That tool allowed the GOP to pass tax reform without the help of Senate Democrats.
Cruz would like to end the Senate's legislative filibuster, a move many members of his own party would not support. The filibuster requires 60 votes to advance major Senate legislation, forcing the chamber to move more slowly than the House, where a simple majority can limit debate.