Washington (CNN) -- The Republican senator who opposes ratification this year of a new nuclear arms treaty with Russia made clear Sunday that politics, not policy, is the main issue.

Arizona Sen. Jon Kyl told NBC's "Meet the Press" program that the Senate won't have enough time in December's "lame-duck" session to properly consider the so-called START treaty with Russia.

According to Kyl, the problem is that Senate Majority Leader Harry Reid, D-Nevada, wants to bring up too many other issues in the lame-duck session before a new Congress convenes in January with a stronger Republican presence.

In particular, Kyl said Reid intends for the Senate to also consider a major immigration bill (the DREAM Act), a repeal of the "don't ask, don't tell" policy barring openly gay and lesbian soldiers from military service, and a measure to make it easier for police and firefighters to form unions -- all of which are opposed by the Republican leadership.

At the same time, the Senate also must take up pressing issues such as Bush-era tax cuts set to expire at the end of the year, and funding the federal government for the rest of the fiscal year, Kyl noted.

"You can't do everything," said Kyl, the second-ranking Republican in the Senate. "How can Harry Reid do everything we talked about and still have time to discuss the START treaty?"

On the same program, Kyl's Democratic counterpart, Sen. Dick Durbin of Illinois, said Americans are tired of Washington gridlock and expect senators to work together to meet all of their responsibilities -- including ratification of the START treaty -- in the lame-duck session.

"We can do all of the things he (Kyl) mentions, debate them and vote on them in a responsible way before we break for Christmas," Durbin said.

Ratification of the START treaty would require approval from two-thirds of the Senate, or 67 votes -- nine more than the 58 seats that will be held by Democrats and their independent allies after Illinois Republican Sen.-elect Mark Kirk gets sworn in Monday.

Kirk won a special election on November 2 to a full Senate term, along with the final days of the term that President Barack Obama vacated when he won the White House two years ago. Democrat Roland Burris, who was appointed to fill Obama's former seat, retired instead of seeking re-election, and Kirk defeated Democrat Alexi Giannoulias in the election.

If the treaty ratification gets put off until next year, Democrats will need 14 Republican votes for ratification because of further losses in the mid-term elections earlier this month.

The START treaty would resume mutual inspections of U.S. and Russian nuclear arsenals, while limiting both nations to 1,550 warheads and 700 launchers each.

Obama has called ratification of the treaty an immediate priority, saying it's critical to national security and a cornerstone of U.S.-Russia relations. Military leaders and GOP Sen. Richard Lugar of Indiana, the ranking member on the Senate Foreign Relations Committee, also call for ratifying START now.

However, 10 GOP senators led by Kyl have urged a delay until the next Congress over concerns about the current Senate workload and the need to modernize the U.S. nuclear arsenal.

Kyl insisted it will take two weeks to properly debate the treaty in the Senate and allow Republicans to propose amendments intended to bolster missile defense capabilities and ensure future funding for updating the U.S. nuclear arsenal. That won't leave time to take up essential issues such as the tax cuts, he said.

Another prominent Republican, Sen. Lindsey Graham of South Carolina, told "FOX News Sunday" the key issue for him was whether the new treaty would limit further development of the U.S. missile defense program. Graham said he and Kyl were concerned that the treaty's preamble includes language that could allow Russia to back out over future development of the missile defense system.

A clear statement from Russia that the United States can develop strategic missile defense systems under the treaty would satisfy his concern, Graham said.

On the same program, Democratic Sen. Claire McCaskill of Missouri accused the Republicans of "game-playing" over the START treaty.

"It's all about politics and it's all about trying to damage the president of the United States," McCaskill said, noting the treaty is supported by NATO allies and prominent Republicans including former Secretaries of State Henry Kissinger, Jim Baker and Colin Powell.

"I can't find anybody in any document anywhere that's saying that somehow that preamble has any impact," McCaskill added. "We are moving ahead with this missile defense, period."

Durbin said on NBC that delaying ratification would send the wrong message to the world, especially a key ally such as Russia that has worked with the United States and other countries in trying to prevent Iran from developing nuclear weapons.

"There is no excuse for us to ignore this responsibility and to say we'll wait several months," Durbin said.

Durbin is a major supporter of the DREAM Act, which would create a path to citizenship for illegal immigrants who entered the United States as children. Under the bill, an individual would have to be of "good moral character" and either receive a college degree or complete at least two years of U.S. military service.

In addition, Obama and the Democratic leadership have pledged to repeal the "don't ask, don't tell" policy, a major issue for the nation's gay constituency. A repeal proposal based on a process agreed to by Obama and military leaders has passed the House and is awaiting Senate consideration as part of a broader military authorization measure.

Graham said on the FOX program that he believes Republicans will remain unified in the lame-duck session to prevent both the DREAM Act and the "don't ask, don't tell" repeal from clearing the Senate.

Arizona Sen. John McCain, who is leading the Republican opposition to "don't ask, don't tell", told CNN's "State of the Union" on Sunday that the controversial policy implemented in 1993 "is working."

"The military is at its highest point in recruitment and retention and professionalism and capability, so to somehow allege that this policy has been damaging the military is simply false," McCain said.

On Tuesday, the Pentagon will release a military review of how to best implement the repeal of "don't ask, don't tell", followed by congressional hearings on the issue. The legislation before Congress would authorize full repeal once Obama, Defense Secretary Robert Gates and Joint Chiefs of Staff Chairman Adm. Mike Mullen certify the review's findings.

McCain, however, called instead for a different report "to assess the effect on the morale and the battle effectiveness" fighting forces on the ground.

Two federal court rulings have found "don't ask, don't tell" to be unconstitutional. Both are being appealed, but the Obama administration and the military leadership want their repeal process contained in the congressional legislation to take place instead of possibly being forced by an eventual final court ruling to suddenly halt the policy.

CNN's Gabriella Schwarz contributed to this story.