In a blog post, Mr. Gonzalez added: “We welcome a rigorous, fact-based debate on the data, methodology and conclusions of the Heritage study on the cost of amnesty. Instead, some have pointed to a Harvard dissertation written by Dr. Jason Richwine.”

Senators piled on amendments Tuesday evening intended to remake — or in some cases thwart — the legislation. The amendments are the greatest test of the bill so far, with provisions from both Democratic supporters of an immigration overhaul and Republicans critics posing potential obstacles before the bill can move out of committee and onto the Senate floor.

One of the most closely watched amendments came from Senator Patrick J. Leahy, Democrat of Vermont and chairman of the Judiciary Committee. He offered two separate amendments that would allow American citizens to seek a permanent resident visa, known as a green card, for a same-sex foreign partner.

Under current law, Americans can gain a green card for a foreign spouse in a traditional marriage relatively easily, but cannot apply for a green card for a gay spouse or partner.

The Republican senators in the bipartisan group that proposed the bill, two of whom sit on the committee, have warned repeatedly that any same-sex amendment would be a deal breaker for many Republicans and could sink the overhaul.

Senator Charles E. Grassley of Iowa, the ranking Republican on the committee, offered 77 amendments, and Senator Jeff Sessions, Republican of Alabama, offered 49. Mr. Sessions has been an outspoken critic of the bill, which he says would harm American workers, and an aide said two of the senator’s amendments would address some of his concerns by capping the number of legal immigrants and foreign workers at 30 million over 10 years.

Senator Mike Lee, Republican of Utah, offered an amendment that would more than double the number of visas offered to low-skilled workers under the bill, a provision that would upset an already delicate deal between the nation’s leading business and labor communities. That agreement would ultimately cap the number at 200,000 annually; Mr. Lee’s amendment would start the program at 200,000 and increase to 400,000.