Mr. Rubio of Florida, who has been discussing for months how to introduce this issue into the Senate, is also eager to raise his national profile. But he must first overcome some of the doubts conservatives have about him for his pivotal role in helping the Senate pass an immigration bill with a provision to eventually grant citizenship to immigrants here illegally.

Mr. Portman of Ohio, who was on Mitt Romney’s short list to become the Republican vice-presidential nominee last year and who has told his colleagues that he would like to be deeply involved in the 20-week legislation, is trying to rebuild conservative support that he lost back home in March after he spoke out in favor of same-sex marriage. (One Republican who saw internal poll numbers after Mr. Portman’s announcement said the senator’s unfavorable ratings jumped by double digits and were especially high in the southern part of Ohio, where his core support is.)