Vaccine Therapy and Sargramostim With or Without Docetaxel in Treating Patients With Metastatic Lung Cancer or Metastatic Colorectal Cancer

You may be eligible if

• Histologically confirmed lung OR colorectal cancer
• Incurable metastatic disease
• Currently available standard treatment not likely to offer a survival advantage or result in superior palliation
• Evaluable disease by radiograph
• Tumor must currently express carcinoembryonic antigen (CEA) by immunohistochemistry OR CEA \>= 10 ng/mL at any point during disease course
• No clinically active brain metastases
• Must have had first- and second-line treatment OR declined second-line treatment (part I only)
• Patients with colon cancer must have had or have been offered treatment with oxaliplatin (part I only)
• ECOG 0-1
• Life expectancy of at least 4 months
• Absolute neutrophil count \>= 1,500/mm\^3
• WBC \>= 3,000/mm\^3
• Platelet count \>= 100,000/mm\^3
• Bilirubin normal
• Meets 1 of the following criteria:
• * SGOT and SGPT =\< 2.5 times upper limit of normal (ULN) AND alkaline phosphatase normal
• * SGOT and SGPT =\< normal AND alkaline phosphatase =\<4.0 times ULN
• Hepatitis B and C negative by clinical history and physical exam
• Creatinine =\< 1.5 mg/dL OR creatinine clearance \>= 60 mL/min
• Proteinuria =\< grade 1
• No known or suspected history of impaired cardiac function as evidenced by baseline echocardiogram
• Adequate pulmonary function
• No history or clinical evidence of immune deficiency or autoimmunity
• HIV negative
• No history of or concurrent diagnosis of any of the following:
• * Altered immunodeficiency
• * Eczema or other eczematoid skin disorders
• * Acute, chronic, or exfoliative skin condition (e.g., atopic dermatitis, burns, impetigo, varicella zoster, severe acne, or other open rashes or wounds)
• No history of allergy or untoward reaction to prior vaccination with vaccinia virus
• No history of severe hypersensitivity reaction to docetaxel or other drugs formulated with polysorbate 80
• No history of allergy to eggs or egg products
• No frequent vomiting or severe anorexia
• No inflammatory bowel disease
• No Crohn's disease
• No ulcerative colitis
• No active diverticulitis
• Neuropathy =\< grade 1 (sensory neuropathy)
• No uncontrolled seizure disorder
• No encephalitis
• No multiple sclerosis
• Must be maintaining a reasonable state of nutrition (=\< 10 % weight loss in the past month)
• Must be able to avoid close household contact (defined as sharing housing or having close physical contact) for at least 3 weeks after recombinant vaccinia vaccination with individuals with active or a history of eczema or other eczematoid skin disorders
• Must be able to avoid close household contact (defined as sharing housing or having close physical contact) for at least 3 weeks after recombinant vaccinia vaccination with those with unresolved acute, chronic, or exfoliative skin conditions (e.g., atopic dermatitis, burns, impetigo, varicella zoster, severe acne, or other open rashes or wounds)
• Must be able to avoid close household contact (defined as sharing housing or having close physical contact) for at least 3 weeks after recombinant vaccinia vaccination with any of the following individuals: pregnant or nursing women; children =\< 5 years of age; immunodeficient or immunosuppressed individuals (by disease or therapy), including HIV infection
• Not pregnant or nursing
• Negative pregnancy test
• Fertile patients must use effective contraception during and for at least 6 months after study participation
• No other concurrent serious medical illness that would preclude study participation
• No concurrent biologic therapy
• No other concurrent immunotherapy
• At least 6 weeks since prior nitrosoureas or mitomycin
• Prior docetaxel allowed (part I only)
• No prior docetaxel (part II only)
• No other concurrent chemotherapy
• No concurrent systemic steroids except for the following:
• * physiologic doses for systemic steroid replacement therapy
• * local (topical, nasal, or inhaled) steroid use
• * no concurrent steroid eye drops
• * premedication prior to and after docetaxel
• No concurrent hormonal therapy
• No prior radiotherapy to \> 50 % of all nodal groups
• More than 21 days since prior major surgery
• No prior splenectomy
• Recovered from prior therapy
• At least 3-4 weeks since prior cytotoxic therapy