The USA PATRIOT Act was passed with near unanimous and bipartisan support (Senate vote, House vote) and signed into law by President George W. Bush on October 26, 2001. Many controversial provisions wisely included sunset clauses which would force Congress to reauthorize them at least once, otherwise they'd expire and no longer be valid law.
Both President Bush and Barack Obama have advocated for those provisions to be repeatedly renewed, but it didn't take very long for a lot of congressmen to regret what they had done.
The first reauthorization came via the USA PATRIOT Improvement and Reauthorization Act of 2005. A majority of Democrats in Congress voted against reauthorizing things like National Security Letters which allow FBI and other agencies to demand credit card and phone records without a court order.
The government originally argued that Congress made NSLs so secret that they forbade any entity or person that received them from discussing them even with their attorneys. Although they eventually backtracked on that after running into lawsuits and an incredulous judiciary concerned that the "gag order" violated the first amendment.
NSLs were found unconstitutional just this past year.
Only 32% (79-164) of Democrats voted to reauthorize the expiring provisions in 2005, while 93% (261-18) of Republicans did.
The second round came in 2006 via the USA PATRIOT Act Additional Reauthorizing Amendments Act of 2006. These weren't all of the provisions that were expiring the previous year, and so doesn't represent a complete referendum on the PATRIOT Act. That said, only 45% (107-127) of Democrats, less than half, voted to renew these provisions. Republicans stepped up their support to 95% (268-13).
The third round came in 2011 via the PATRIOT Sunsets Extension Act of 2011. 40% (90-135) of Democrats voted in favor and 87% of Republicans (238-35).
Despite what President Obama has done to expand the national security and surveillance state, and efforts of some national security hawks on the left, the Democratic Party in Congress almost immediately regretted voting for the signature surveillance state legislation of the past two decades, while Republicans have enthusiastically supported it even to this day.
The GOP-controlled House of Representatives has been working for months to pass a new "Cybersecurity" bill that would further increase the spying powers of the federal government and further weaken civil liberties. (88% of Republicans voted for the bill, while 76% of Democrats voted against it.)
This is a wide-ranging issue that can't be boiled down to Republicans suck and Democrats rule on domestic spying, but that doesn't mean that the two major political parties are equally enthusiastic about it. That is not the case, especially with the PATRIOT Act.