Gingrich and company at least tried in 1995. It took a two thirds vote to enact term limits so even if every Republican had voted in favor, it still would not have passed.
They take some grief for promising term limits and not delivering but the contract only said they would bring it up for a vote, and they did. Sadly it didn’t make it. A large majority of Republicans voted for it at least. But I suppose there was never a realistic chance it would pass.
As I recall, the proposed Term Limit amendment got 65 votes in the Senate. A total of 66 were required to send the amendment to the states. I believe all but one GOP senator voted in favor of the amendment.