A Republican senator warned Tuesday that a bipartisan immigration-reform proposal now under consideration would allow illegal immigrants to take advantage of government welfare benefits much sooner than the 13-year time frame outlined in the legislation.

Sen. Jeff Sessions, R-Ala., said loopholes in the legislation would permit those who came to the U.S. illegally to collect cash assistance, food stamps and health care benefits long before they earn a green card and a pathway to citizenship.

Sessions and other critics of the bill believe it will drive up government spending on social programs. Newly legalized immigrants may not have immediate access to federal benefits, but many states don't stop them from getting cash assistance, health care and other benefits.

"Dozens of states currently offer public benefits to 'lawfully present' aliens, and illegal immigrants seeking [legal] status are not precluded from using them," Sessions said.

Sessions said millions of illegal immigrants will be on a much faster track to attain federal benefits like welfare, Medicare and Medicaid because they came to the United States as children or work as farm laborers. If family members join the immigrant in the U.S., a common occurrence, it would drive up benefit costs even more, Sessions said.

The cost of immigration reform will be a top issue when Congress returns next week. Senators will resume committee consideration of the Border Security, Economic Opportunity, and Immigration Modernization Act of 2013, an 800-page bill that couples increased border security with instant legalization and a pathway to citizenship for the 11 million illegal immigrants already in the U.S.

The bipartisan "Gang of Eight," which helped author the bill, has promised it would be "revenue neutral," meaning it will not add to the debt.

Fears that the bill will add millions to the federal benefits rolls are unfounded, proponents say, because most immigrants won't be eligible for them until they work a full decade and attain a green card.

One of those lawmakers, Sen. Charles Schumer, D-N.Y., said that once the Congressional Budget Office works out the cost of immigration reform, Congress can raise any fees or penalties in the law to cover costs and ensure it's "revenue neutral."

Sessions will attempt to amend the immigration bill once the Senate takes it up "to address the legislation's enormous federal costs and to ensure that illegal immigrants will not become dependent on already burdened state and local benefit programs."

Sen. Marco Rubio, R-Fla., a Gang of Eight member, signaled Tuesday he is open to such changes.

Rubio said on the Mike Gallagher radio show that the bill is "a starting point" and that he has heard "valid objections" that should be addressed as the bill advances.

Alex Nowrasteh, an immigration policy analyst at the Cato Institute's Center for Global Liberty and Prosperity, said Sessions is "vastly" exaggerating the cost of the reforms and that state benefits would not be available to newly legalized immigrants until they obtain green cards.

Nowrasteh acknowledged, however, that illegal immigrants who arrived as children and those who are part of the agricultural worker program would be on a faster track to obtain benefits than other illegals.

"They would be eligible sooner," Nowrasteh said, "but not right off the bat."